Grabovski, 29, has been a free agent since the Toronto Maple Leafs used a compliance buyout July 4. He had four seasons and $21.5 million remaining on a five-year contract.
"Mikhail adds speed and offense to our lineup, and we are very pleased to have him sign with the Capitals," general manager George McPhee said in a statement. "We believe he will be an excellent addition to our club."
After starting the 2012-13 season with CSKA Moscow of the Kontinental Hockey League, Grabovski had 16 points (nine goals) in 48 games for Toronto. Grabovski fell out of favor with Toronto coach Randy Carlyle, but he is a favorite of the advanced-statistics community because of his ability to drive puck possession.
SOG: 80 | +/-: -10
He also played less. Grabovski averaged 19:22 of ice time in 2010-11 and 17:36 in 2011-12, but his average TOI dipped to 15:34 last season. Grabovski did average more than 19 minutes per game (19:06) during Toronto's first-round Stanley Cup Playoff series loss to the Boston Bruins, which placed him third on the Maple Leafs among forwards.
Despite that, Grabovski had the second-highest corsi rating relative to the quality of competition among Toronto forwards behind Nikolai Kulemin, according to the site Behind the Net.
In 367 NHL games with the Maple Leafs and Montreal Canadiens, Grabovski has 94 goals and 217 points. He had at least 20 goals and 48 points three times for the Maple Leafs, including 29 goals and 58 points in 2010-11.
The Capitals have yet to sign restricted free agent Marcus Johansson. If he signs, the Capitals could keep their top line from the second-half of last season (Backstrom flanked by Johansson and captain Alex Ovechkin) together. Brooks Laich, who was slated to be the No. 2 center before Grabovski's arrival, has been a versatile player for the Capitals and could end up on the wing of the one of the top two lines or as the No. 3 center.