Jeff Green will return to Washington where he played in college with Georgetown. (Sue Ogrocki/Associated Press)

During the NBA Eastern Conference finals, Jeff Green certainly had his mind on his Cleveland Cavaliers as they contested the Boston Celtics in a tight playoff matchup. However, like anyone with Washington roots, Green also obsessed over the Capitals’ run to the Stanley Cup. On the night before the Capitals played in the Game 1 of the finals, Green vowed to be in front of his television. Next season, however, Green can probably get a more up-close view of his favorite hockey team.

On Tuesday, Green reached a one-year deal with the Washington Wizards, giving the team a veteran backup forward with NBA Finals experience.

Green, the 31-year-old native of Hyattsville, has career averages of 13.2 points, 4.6 rebounds and 1.6 assists. With the decision to sign with the Wizards, Green returns to the same arena in which he starred as a member of the Georgetown Hoyas for three seasons.

In 2007, Green was the fifth overall pick. Three years into his career, he formed a young core with rising superstars Kevin Durant, Russell Westbrook and James Harden for the Oklahoma City Thunder, coached by Scott Brooks. However, years later, Green’s career was sidetracked when he required open-heart surgery to repair an aortic root aneurysm. After missing the entire 2011-12 season, Green played stints with Boston, Memphis, Los Angeles (Clippers) and Orlando.

“Each day I give it my all, whether good or bad. I live with the results,” Green said back in May, recalling how the health scare impacted his mind-set. “But I am enjoying it, every single moment of this. … I don’t take nothing for granted. Nothing.”

Green’s latest stop in Cleveland provided a seminal moment.

Last season, Green appeared in 78 games and made 13 starts for the Cavaliers. His highlight came during the team’s last big win of the playoffs. In Game 7 of the conference finals, Green stepped in as a starter in place of the injured Kevin Love, playing almost 42 minutes and scoring 19 points on 7-of-14 shooting. After the Cavaliers secured the win and advanced to the Finals, teammate LeBron James put Green’s journey in perspective.

“This guy had open-heart surgery a few years ago. The game was basically taken away from him, and they said it’s possible you’ll never play the game of basketball again,” James said after the game. “The fact that he can put on a uniform every day and do the things that he does out on the floor — for him personally, it’s the cherry on top because the game was taken away from him.”

James has since moved on to play with the Los Angeles Lakers, while Green makes a homecoming to the origins of his basketball story.