The person, who spoke on condition of anonymity because the Giants haven't announced the deals, told The Associated Press that the starters and the team just finished work on the contracts.
NFL Network first reported the agreements and said Webster took a $3 million pay cut. He had a disappointing 2012 season and will earn $4 million in the final year of his contract.
NFL Network also said Baas re-structured his five-year contract. He still will earn $4.25 million in third year but his base pay was lowered to $1.25 million. The other $3 million will come as a signing bonus.
The moves combined will clear roughly $6 million in cap space for the Giants, giving them $9 million for free agency.
The Giants, who missed the playoffs with a 9-7 record after winning the Super Bowl the previous season, could create more space if they rework tackle David Diehl's contract. He is due to make $4.475 million this season, and also had a sub-par year in 2012.
New York may need more money with receiver Victor Cruz, halfback Andre Brown and safety Stevie Brown all being restricted free agents.
The 31-year-old Webster had 58 tackles, 13 passes defended and four interceptions last season for a defense that was ranked next to last in the league. However, he also saw receivers that he was covering catch at least a half-dozen touchdowns.
Joe Flacco and the Super Bowl champion Baltimore Ravens targeted Webster late in the season in a 33-14 win over New York, with receiver Torrey Smith beating the former LSU star for their first touchdown.
Webster played a major role in the Giants two recent Super Bowl titles, with his interception of a Brett Favre pass in overtime, setting up Lawrence Tynes game-winning field goal in the NFC title game against the Green Bay Packers early in 2008.
Baas was signed as a free agent after the Giants released Shaun O'Hara after the NFL lockout ended before the 2011 season. He has started the past two seasons but also has been limited by nagging injuries in his short tenure.