Jaden Springer, left, and Xavier Tillman, both acquired in trades by the Celtics before the deadline, watch Boston’s game against Washington on Friday. Michael Dwyer/Associated Press

Before he was traded to the Celtics this week, Xavier Tillman already had a good idea of what it will take to thrive in his new home. A former member of the Grizzlies, he was in town on Sunday when the Celtics honored former guard Marcus Smart, who received overwhelming love from the fans. Smart, who was sent to Memphis as part of a three-team trade, had described to Tillman how he earned that feeling.

“The main thing he told me (is) it’s very similar to Memphis in terms of the grit and the grind and how hard you have to work for the fans and appreciation and stuff like that,” Tillman said. “And once you do show that you’re willing to hustle, they’re gonna love you. I love it.”

Tillman, who was traded to the Celtics on Wednesday, participated in his shootaround with the team prior to the Celtics’ 133-129 win over the Wizards on Friday. He did not suit up, still recovering from the left knee soreness that forced him to miss his final four games with the Grizzlies, so he’ll have to wait to earn that love from his new fanbase. But he’s certainly excited to be with the Celtics in their pursuit of a championship.

“It’s crazy, to be honest with you,” Tillman said. “I’ve always watched the Celtics in terms of just the winning history of it, back with (Kevin Garnett) and all that stuff and seeing these guys repeatedly go to the Eastern Conference Finals all the time, I’m always locked in on that. So for me to get the opportunity to be part of a winning organization, it’s pretty awesome.”

It’s unclear when Tillman will make his Celtics debut. He said he still needs some time to recover.

“I don’t have a timeline,” Tillman said. “We’re actually just getting here and meeting with the trainers and stuff like that. So we’ll go through it pretty soon here.”

When he’s at full health, Tillman is expected to serve as valuable depth in the Celtics’ frontcourt behind Kristaps Porzingis and Al Horford. Celtics President of Basketball Operations Brad Stevens said the addition of Tillman should give them more flexibility and options with their lineups, and his presence should help give Porzingis and Horford some rest as the Celtics aim to preserve those two for a long playoff run.

Tillman will be an asset for the Celtics defensively, capable of guarding multiple positions and giving them some added rim protection. There will be an adjustment period as he learns the Celtics’ language and schemes, but he doesn’t think it will be overly challenging.

“Coming out of the film session, that’s something that I was learning and stuff like that, the nuances of how they like to operate and stuff like that,” Tillman said. “It’ll take a little bit but I don’t think it’ll be too long or too hard for me to get adjusted to it for sure.”