The agreement came at a time when agent Bill Strickland was setting up meetings with three other teams - Orlando, San Antonio and Dallas.

Wallace - after going over the Celtics' offer with his wife Fatima, who was present at a meeting between the Celtics and the former Piston's camp last Thursday in Detroit - called Strickland yesterday afternoon to say he wanted to end the process and sign with the Celtics .

The reason, Strickland reiterated, was the fact that Wallace considers the Celtics his best chance to win another championship ring.

``Rasheed took the first meeting very well, and was impressed once it became clear that we were all talking about the same financial situation,'' said Strickland. ``He obviously likes the team, and the meeting was very effective.

``Once he started evaluating everything, he just made a decision that this was where he would like to play next.''

Orlando general manager Otis Smith had said on Friday that he wanted to schedule a meeting with Wallace.

``I had spoken with all of the other teams,'' said Strickland, who earlier yesterday had said via text message that the Mavericks, despite agreeing with Marcin Gortat to a five-year, mid-level deal, were still in the running.

Though the Celtics came away from last week's meeting with the impression that Wallace would need time to make a decision - especially considering that he planned to meet with representatives of four other teams - they requested expediency. That was due to general manager Danny Ainge's continued search for free-agent talent, with both the $1.3 veteran's minimum and $1.9 million biannual exception to spend on further frontcourt help.

Big men and backup small forward help are a priority, which explains the team's plan to meet with Grant Hill.

Coach Doc Rivers, who lives close to his former Magic forward - now a free agent who played for Phoenix last season - acknowledged yesterday that he will soon meet with Hill.

Hill, via a local media outlet, confirmed Saturday that he is planning to meet with Rivers.

``We live close to each other,'' Rivers said yesterday. ``So that's not such a big deal. We see each other all the time.''

But with Wallace now under agreement, the Celtics have more to do. Ainge's vow to continue improving the team contributed to Wallace's decision to sign with the Celtics .

In addition to Hill, Ainge has targeted guard Tyron Lue.

There is also the pressing issue of Glen Davis, a restricted free agent who is expected to draw attention from many of the same teams.

``They asked Sheed to consider making a decision soon because they wanted to get other things wrapped up,'' said Strickland.

Wallace, who later told Strickland that he was impressed with everything - from the presence of Kevin Garnett, Paul Pierce and Ray Allen at the meeting, to the presence of co-owner Wyc Grousbeck - found the Celtics' request easy to honor.

And the Celtics now have one of the best shooting big men in the NBA - one who can stretch the floor, defend the post, and spell both Garnett and Kendrick Perkins.

Also, a player who is expected to give a serious boost to everyone's only goal, his own included - another ring.

- mrmurphy@bostonherald.com