Mikhail Grabovski spins around Capitals goalie Michal Neuvirth before scorinhg a shootout winner in December 2010. (Toni L. Sandys/THE WASHINGTON POST)

When Coach Adam Oates visited Los Angeles 10 days ago to meet with Mikhail Grabovski and make a case for why the unrestricted free agent center should strongly consider joining the Washington Capitals, he was blunt.

He knew that the Capitals were one of a dozen teams pursuing Grabovski and the 29-year-old had his pick. But Oates believed in the opportunity for both the team, which was in need of depth at center, and the player, who needed a fresh start, to help each other improve.

“I told him the facts of life from the Capitals’ point of view, from my point of view,” Oates said. “I told him I think he fits into our puzzle.”

Grabovski, who grew up in Belarus, ultimately concurred with Oates’s assessment, signing a one-year, $3 million contract with Washington on Friday.

It’s a salary-cap friendly addition for the Capitals that bolsters the middle of the lineup with a player who has demonstrated he can be a 50-point producer when in a top-six role. And it gives Grabovski a chance to re-establish himself as a consistent offensive presence with significant playing time after falling out of favor with Maple Leafs Coach Randy Carlyle last season and seeing both his role and scoring diminish.

“It’s a win-win in the sense that for him, he’s coming to a team that has good players to play with him,” Oates said. “We’ve got some guys that I think we can complement him with that will do very well, and he will benefit from that. And we’re going to use what he brings to help benefit us.”

Said Grabovski: “I like the system, I like [the fact] the team really wants me. . . . I chose Washington because they really trust me and I think I can help them.”

When Mike Ribeiro signed with the Phoenix Coyotes as a free agent earlier this summer, it left a glaring vacancy at second-line center. The Capitals have used eight players in that role since 2009, including some candidates who are still on the roster, but last season illustrated the intrinsic value of center depth at the top of the lineup.

In early July, Grabovski became an unexpected free agent after Toronto bought out the final four years and $21 million in his contract. It was a sour ending to a lackluster season (nine goals, 16 points in 48 games) and an abrupt conclusion to his rocky relationship with Carlyle, who Grabovski called an “[expletive] idiot” in an interview with TSN.

It was around the same time that Capitals General Manager George McPhee named Brooks Laich as second-line center.

Laich, 30, had played the position before and was the logical solution at the time. McPhee’s statement didn’t stop speculation that Grabovski could be a solution for the Capitals, though, and nearly two months later the two sides came to a deal.

“On July 8 [Laich] was our No. 2 center, but things change over the course of the summer,” McPhee said. “It looked like there was an opportunity with Grabovski and really having Brooks, knowing that he could play that position allowed us to do this deal. We could take our time and get the right deal.”

Grabovski isn’t as smooth of a setup artist as Ribeiro, but he has more of a two-way skill set and should help provide balance on the second line. His inclusion creates lineup options for Oates and allows Laich to continue serving as the team’s most versatile forward, playing on any line as a left wing or center as necessary.

“It’s great. I think we needed him,” first-line center Nicklas Backstrom said. “He’s been really good in Toronto, I think personally, so we’re excited to have him come in.”

In his first four seasons with Toronto before last year’s slide, Grabovski recorded three 20-goal seasons, posted a career-high 58 points in 2010-11 and often centered the second line. The Capitals believe Grabovski can return to that type of production if given the opportunity to earn the playing time and additional responsibility that he lacked during his struggles last year.

During their meeting in Los Angeles, Oates made it clear he would offer “every opportunity” for Grabovski to excel. That sentiment made a strong impression on Grabovski.

“I try my best to prove myself and play better than last year,” Grabovski said. “I think [Oates] understand me. For me, I just need to work hard and try and play my best and show coach how I am as a player.”