LOS ANGELES — Before Aaron Rodgers teed off this week at the 16th hole of a pro-am event in Arizona, an announcer introduced him as a three-time winner of the N.F.L.’s Most Valuable Player Award. Without hesitating, Rodgers flashed four fingers instead.

Whether it was prescience, a reasonable conclusion or a cheeky revelation of insider knowledge, his prediction came true on Thursday. On the same night that the Pro Football Hall of Fame welcomed eight new members, Rodgers further enhanced his credentials for eventual enshrinement.

In winning his fourth M.V.P. award, Rodgers now trails only Peyton Manning, who has five, on the career list. He also joined Jim Brown, Joe Montana, Brett Favre and Manning as the only players to win consecutive M.V.P. awards.

Despite playing much of the season behind a makeshift offensive line, Rodgers finished with 4,115 passing yards, 37 touchdown passes and four interceptions in leading the Green Bay Packers to an N.F.C. North title and the conference’s No. 1 seed in the playoffs.

The Packers flopped in the postseason, though, losing in the divisional round at home to San Francisco — and, after that game, Rodgers acknowledged his uncertainty about returning for an 18th season with Green Bay. But Coach Matt LaFleur and the team’s president, Mark Murphy, have stressed that they want Rodgers back.

Through concessions the team has made with his contract, Rodgers, 38, has the power to determine whether to seek a trade. After that loss to San Francisco, he also acknowledged the possibility, however less likely, of him retiring.

This year’s group of Hall of Famers was headlined by the posthumous selection of linebacker Sam Mills, who was in his 20th and final year of eligibility as a candidate from the modern era.

Two defensive linemen — Bryant Young of San Francisco and Richard Seymour, who played for the New England Patriots and the Oakland Raiders — were also selected in voting, which was conducted last month by a panel of 49 members of the news media. Joining them were Packers safety LeRoy Butler, who was in his 16th year of eligibility, and Jacksonville Jaguars offensive tackle Tony Boselli, who had been a finalist for the last six years.

The selection committee also elected three members: the coach Dick Vermeil, who won a Super Bowl with the Rams in the 1999 season; Art McNally, a supervisor of officials, who was the contributor finalist; and Cliff Branch, the Raiders receiver, who was the senior finalist.

Mills, who died of stomach cancer in 2005, went undrafted out of Montclair State, a Division III program, but emerged as a star in the United States Football League before latching on with the Saints in 1986. He reached four out of his five Pro Bowls with New Orleans before finishing his career with the Carolina Panthers, who adopted their “Keep Pounding” mantra after Mills urged them to do so during the team’s N.F.C. title run in 2003.

Seymour, one of Patriots Coach Bill Belichick’s favorite players, had 57.5 sacks across his 12 seasons, more than any other defensive tackle. A three-time Super Bowl winner, he also made the league’s All-Decade team of the 2000s.

Another dominant interior lineman voted onto an all-decade team, Young overcame a gruesome leg injury in his fifth season to finish his 14-year career with four All-Pro selections and 89.5 sacks.

Butler joined the recent surge of safeties inducted into the Hall, following John Lynch and Steve Atwater. Until Thursday, Butler, who helped restore the Packers to relevance during his 12 seasons in Green Bay, had been the only first-team member of the 1990s All-Decade team yet to be inducted. A four-time first-team All-Pro, he was credited with pioneering the Lambeau Leap — and had 38 interceptions and 20.5 sacks.

Boselli, the first player selected by the expansion Jaguars in 1995, dominated at left tackle over a career that spanned only six full seasons. He was named to the league’s All-Pro team three times and its team of the 1990s despite playing only the second half of the decade.

Boselli benefited this year from a logjam clearing along the offensive line, with Alan Faneca, Steve Hutchinson and Kevin Mawae gaining induction in the previous three classes.

None of the three finalists in their first year of eligibility — receiver Andre Johnson, defensive end DeMarcus Ware and return specialist Devin Hester — were tapped, suggesting a desire by voters to induct players who had been waiting a while.