After remaining in Russia for the 1992-1993 season with the Moscow Dynamo, Yashin arrived in Ottawa for the 1993-94 season, the same year as Ottawa's other touted young phenom, Alexandre Daigle. Yashin soon eclipsed Daigle as Ottawa's brightest young star, scoring 79 points in his rookie season and earning himself a nomination for the Calder Trophy.
Subsequent seasons in Ottawa saw him emerge as an NHL superstar, helping Ottawa to make the playoffs for the first time in 1997. In 1998, he scored a key overtime goal for the franchise that helped secure their first ever playoff series victory against the New Jersey Devils.
Yashin was eventually named team captain, and the pinnacle of his career came in the 1999 season when he scored 94 points and was a runner-up for both the Hart Trophy for the NHL's most valuable player, and the Richard Trophy for the NHL's highest goal scorer.
Off the ice, however, Yashin's stay in Ottawa was tumultuous. Several nasty contract disputes developed between Yashin and the team, beginning when Yashin refused to play the start of the 1995-1996 season unless he was given a contract similar to the glitzy contract that the popular Daigle had signed. Tensions reached a high point after the 1998-1999 season, when Yashin refused to honour his contract, which had one year remaining. The team refused to tear up the contract, and Yashin spent the entire 1999-2000 season practicing with a team in Switzerland. While the Senators regressed that year, Yashin turned out the ultimate loser, as an NHL legal panel ruled that he still owed the Senators one more season with the current contract.
Yashin returned to the team in 2000, but the captaincy had been given to teammate Daniel Alfredsson. After the Senators were swept in the first round of the playoffs by the Toronto Maple Leafs, it was clear that Yashin had played his last game for the Senators.
On draft day, 2001, Yashin was traded to the New York Islanders for Zdeno Chara, Bill Muckalt and the 2nd overall draft selection, which the Senators used to draft Jason Spezza. The Islanders promptly signed the 27-year old Yashin to an enormous 10-year 87.5 million USD contract.
Since joining the Islanders, Yashin's point production has declined. While he helped his new team make the playoffs for the first time in years, the team has been unable to make it past the first round of the playoffs, losing in 2002 to the Toronto Maple Leafs and in 2003 to his old team, the Ottawa Senators. Yashin's play has been criticized by fans, teammates and coaches - at one point he was demoted to New York's fourth line.
Yashin is married to supermodel Carol Alt.