A source close to Davis told ESPNNewYork.com's Ian Begley that the veteran point guard flew into New York on Sunday night and is expected to be at the Knicks facility on Monday to finalize his contract.
Davis cleared waivers Friday after he was released through the amnesty clause in the new labor agreement by the Cleveland Cavaliers.
SI.com reported that Davis and the Knicks have agreed to a one-year deal worth $2.5 million, which is the maximum New York could pay in using what is known as the "mini" mid-level exception for luxury-tax teams.
But it remains to be seen how soon Davis will be able to play for the Knicks thanks to a back injury that the Cavaliers, upon releasing him, believed would sideline the former All-Star for eight to 10 weeks.
The Knicks, though, chased Davis aggressively despite the injury, desperate to upgrade their backcourt to support a frontcourt duo of Carmelo Anthony and Amare Stoudemire that was recently boosted the arrival of Tyson Chandler to be the Knicks' defensive anchor.
The team has penciled in Toney Douglas as its starting point guard and Mike Bibby as a backup. But with Douglas lacking experience and Bibby coming off of a subpar playoff run with the Miami Heat, the Knicks have been interested in bringing in Davis as another option at point guard.
Anthony was excited about adding a possibly healthy Davis.
"Everybody knows what he can do when he's healthy and when he's focused," he said, before news of the deal was announced. "I was here for two months last year and we played (the Cavaliers) quite a bit of time when I got here and he was healthy then. They beat us and he was a big part of those wins.
"When BD (Davis) is healthy, he's one of the best."
The Los Angeles Lakers and Heat also expressed strong interest in signing Davis, who was waived Wednesday night by the Cavs.
Teams with salary-cap space had the right to bid on Davis in the 48 hours before he cleared waivers but elected not to, presumably because of the back injury. The waiver auction for teams with cap space is the mechanism that allowed the Los Angeles Clippers to put in a winning blind bid of a little more than $2 million for Chauncey Billups after Billups was released by the Knicks via amnesty.
ESPN The Magazine's Ric Bucher, quoting one source close to the situation, reported Saturday that the initial diagnosis may have been too conservative and that Davis could be back in four to six weeks.
Sources say Davis, 32, always intended to make a decision well before he's physically able to play so he can familiarize himself with the team's playbook and personnel and settle into his new home.
ESPN.com reported in early November, furthermore, that Davis regards playing at Madison Square Garden on par with playing with the Lakers in terms of his lifelong dreams.
On Saturday, Bucher quoted the source saying: "Going to a team that really wants (Baron) is an important part of it."
Rougly $27 million of the nearly $30 million left on Davis' contract is guaranteed. The Cavs still have to pay Davis that money even after sending him away, but the new amnesty clause -- unlike the 2005 version -- give teams salary cap relief as well as tax relief on a player released via amnesty.
The immediate priority for Davis is getting healthy. The back injury has kept Davis off the floor since training camps opened last week and Davis' agent, Todd Ramasar, told ESPNNewYork.com's Ian Begley that "Baron is out a minimum of eight to 10 weeks if there's no setbacks in his physical therapy."
The Cavs weighed whether to keep Davis for one more season and try to play him alongside No. 1 overall pick Kyrie Irving. Cleveland coach Byron Scott, who had Davis in New Orleans, had also spoken optimistically of the idea that Irving and Davis could function well together in the same backcourt.
Yet the overriding sentiment within the organization calls for handing the keys of the franchise to Irving right away. With Ramon Sessions on the books in Cleveland for two more seasons at a cap-friendly salary and Daniel Gibson coming off his best season, letting Davis go now eases a potential backcourt logjam.
Davis arrived in Cleveland in February in a trade-deadline deal for Mo Williams that was clinched by the Clippers' willingness to include their first overall pick in the June draft unprotected. That pick became Irving.
Davis averaged 13.1 points and 6.7 assists in 58 games for the Clippers and Cleveland last season.
"We would like to thank Baron for his contributions to the team during his time in Cleveland," Cavs general manager Chris Grant said in a statement Wednesday night. "He has been an absolute professional since the day he joined the Cavs and we now wish him the best in the future."
Marc Stein is a senior writer for ESPN.com. Dave McMenamin covers the NBA for ESPNLosAngeles.com. Information from ESPN The Magazine's Ric Bucher, ESPNNewYork.com's Ian Begley and ESPN.com's Brian Windhorst was used in this report.