WASHINGTON — NFL players voted to OK a final deal Monday, days after the owners approved a tentative agreement, and the sides finally managed to put an end to the 4½-month lockout, the longest work stoppage in league history.

“This is a long time coming, and football’s back,” NFL Commissioner Roger Goodell said, “and that’s the great news for everybody.”

At a joint appearance outside the NFL Players Association headquarters, Goodell and NFLPA head DeMaurice Smith were flanked by some of the owners and players who were involved in the talks. They spoke shortly after the NFLPA executive board and 32 team reps voted unanimously to approve the terms of a deal.

“We didn’t get everything that either side wanted … but we did arrive at a deal that we think is fair and balanced,” Smith said.

Owners overwhelmingly approved a proposal Thursday, but some unresolved issues still needed to be reviewed to satisfy players; the owners do not need to vote again.

The sides worked through the weekend and wrapped up the details Monday morning on a final pact that runs for 10 years and doesn’t include an opt-out clause.

With an agreement in place, work begins for the league’s 32 clubs almost immediately. The NFL will distribute a list of free agents to teams Monday and players can begin to report to team facilities for physicals, meetings and to receive playbooks Tuesday.

Also on Tuesday, teams can start signing 2011 draft picks and undrafted rookie free agents at 10 a.m. ET. They also can begin making trades at that time and begin conversations with veteran free agents from all teams. However, no player can officially sign until Friday at 6 p.m. ET. Teams will not have a window to negotiate exclusively with their own free agents.

However, when veteran free agents do sign with teams, they will not be able to participate in any practice, weight training or workouts until the beginning of the league year, slated to be Aug. 4. They will be required to attend classroom sessions and non-physical activity once the contracts are signed.

Rookies, both drafted and undrafted, will be allowed to fully participate and their contracts will be fully covered, regardless of whether the agreement is ratified.

Then, beginning Wednesday, the first group of teams will report for training camps, 15 days before each club’s first preseason game.

The first 10 teams are: Seattle, San Diego, Arizona, Oakland, Denver, Dallas, Jacksonville, Baltimore, Philadelphia, New England.

On Thursday, 10 more teams will report: Tampa Bay, Kansas City, Miami, Atlanta, San Francisco, New Orleans, Pittsburgh, Washington, Cincinnati, Detroit.

And Friday, 10 additional teams will report: Buffalo, Chicago, Green Bay, Cleveland, Indianapolis, St. Louis, Minnesota, Tennessee, NY Giants, Carolina.

The New York Jets and Houston Texans will be the last two teams to report, on Sunday.

Teams have until 4 p.m. ET on Thursday to waive or cut players.

The league year is scheduled to begin on Aug. 4 if the agreement has been ratified by the NFLPA, which must first re-establish itself as a union. By that date, all teams must also be under the salary cap.

Indianapolis Colts quarterback Peyton Manning, one of the 10 named plaintiffs in the players’ antitrust lawsuit against the NFL, said in a statement, “I want to get back to work.”

“My objectives were two-fold when joining the group of named plaintiffs in the labor-related lawsuit. First, to show unified strength on behalf of benefitting all players; second, to see a resolution that recognizes the interests of players and management. I believe both objectives have been achieved,” Manning said in the statement. “As a fan of the game, I’m pleased the two sides have reached a deal and, as a professional, I want to get back to work.”

Manning was invited to attend the NFLPA press conference Monday but said he was unable to do so because of his rehabilitation and therapy recovering from neck surgery on May 23 to repair a bulging disk.

Owners decided in 2008 to opt out of the league’s old labor contract, which expired March 11. That’s when the owners locked out the players, creating the NFL’s first work stoppage since 1987.

“I know it has been a very long process since the day we stood here that night in March,” Smith said. “But our guys stood together when nobody thought we would. And football is back because of it.”

As he spoke, Smith was flanked by NFLPA presidentKevin Mawae, Saints quarterback Drew Brees, Colts center Jeff Saturday and Ravens defensive backDomonique Foxworth, key members of the players’ negotiating team.

“I believe it’s important that we talk about the future of football as a partnership,” Smith said.

Moments later, Goodell walked into the building, joined by owners Bob Kraft of the New England Patriots, John Mara of the New York Giants and Jerry Richardson of the Carolina Panthers.

Kraft apologized to fans for having to wait out the labor turmoil.

“The end result is we’ve been able to have an agreement that I think is going to allow this sport to flourish over the next decade,” Kraft said.

In a touching moment during the news conference, Saturday hugged Kraft and said, “without him, this deal does not get done.”

Both sides set up informational conference calls for Monday afternoon to go over the details of the agreement. The NFLPA told player agents they would be coached in particular on the guidelines and schedule for signing free agents and rookies; the NFL alerted general managers and coaches they would be briefed in separate calls.

Smith, who hopes to mend fences with NFL’s retired players, had a conference call Monday morning with the former players to share with them the gains that they made in this deal, including the unprecedented “legacy fund.”

The major economic framework for the deal was worked out more than a week ago.

That included how the more than $9 billion in annual league revenues will be divided (about 53 percent to owners and 47 percent to players over the next decade; the old CBA resulted in nearly a 50-50 split); a per-club cap of about $120 million for salary and bonuses in 2011 — and at least that in 2012 and 2013 — plus about $22 million for benefits; a salary system to rein in spending on first-round draft picks; and unrestricted free agency for most players after four seasons.

The final process for negotiating the new collective bargaining agreement will begin after the NFLPA recertifies as a union. Benefits and health care, handling of grievances and the substance-abuse policy are all things that players will negotiate after they reform as a union, but the lack of a CBA will not hold up 2011 league business from beginning.