Moriyasu was educated at and played for Nagasaki Nihon Daigaku Gakuen High School. After finishing his school, he joined Japan Soccer League side Mazda in 1987. New manager Hans Ooft rated him highly and established him as an anchoring midfielder of the team. In April 1990, Moriyasu had a trial at Manchester United. When Japan's first ever professional league J. League Division 1 started in 1993, Mazda was transformed to Sanfrecce Hiroshima for whom he continued to play. Together with Yahiro Kazama, he controlled Hiroshima's midfield and contributed to the club winning the second stage of the 1994 J. League season.
In 1998, Ooft became the manager of Kyoto Purple Sanga and recruited Moriyasu on a loan deal. The deal was initially meant to be a permanent one but infuriated Hiroshima supporters collected signatures against the deal, which forced the clubs to settle for a loan. He was the linchpin of Kyoto for the 1998 season.
Moriyasu came back to Hiroshima for the 1999 season but find out his opportunities to play gradually decreasing mainly because of young Kazuyuki Morisaki's challenge for the place.
He was offered a coaching position at Hiroshima in 2002 but turned it down to continue to play. He moved to Vegalta Sendai and retired there at the end of the 2003 season.
Ooft became the national coach of Japan in 1992. He called up and played Moriyasu for his first match in charge against Argentina held on May 31, 1992 at the Tokyo National Olympic Stadium. Moriyasu was still a low-profile player at that time and many international teammates didn't know how to pronounce his name. What Ooft asked him to do throughout his reign was a simple task, to "win the ball and pass it to playmaker Ruy Ramos".
He was a member of the Japan team that won the 1992 AFC Asian Cup and played all the Japan games except the final against Saudi Arabia for which he was ineligible due to suspension.
Under Ooft, Japan progressed to the final qualifying stage of the AFC for the 1994 FIFA World Cup. Moriyasu was on the pitch when Japan's hope to play in the finals was dashed by an injury time Iraqi equaliser in the last qualifier, the match that the Japanese fans now refer to as the Agony of Doha.
He was capped 35 times between 1992 and 1996. He scored one goal for his country in a friendly against Australia on February 10, 1996.
He served as a coach for Sanfrecce Hiroshima from the 2004 season. He also coached the Japan national youth team which participated in the 2006 AFC Youth Championship and the 2007 FIFA U-20 World Cup. He was a coach for the Hiroshima first team from 2007 to 2009 before a spell coaching at Albirex Niigata.
It was confirmed on 8 December 2011 that Moriyasu would return to Sanfrecce Hiroshima as manager for the 2012 season. Since then, he has won the J league title for both the 2012 season and the 2013 season.