Lambert started nine games last season, completing 59% of his passes for 1,632 yards, 10 touchdowns and 11 interceptions. Junior quarterback Matt Johns surpassed Lambert claimed the top spot on the depth chart following spring football.
Lambert said the transfer was the "hardest decision" of his life.
Johns also received significant playing time last season, completing 54.9% of his passes for 1,109 yards, eight touchdowns and five interceptions.
Virginia coach Mike London, who said after spring football that the decision to put Johns on top of the depth chart "wasn't close," said that he met with Lambert about the transfer earlier this week.
"I met with Greyson earlier this week and he explained to me his reasons for wishing to transfer," London said, according to ESPN. "I want to wish him well and appreciate everything he has done for our football program. He is a fine young man and will do well."
The Cavaliers finished last season 5-7, the team's third straight losing season. Virginia opens its 2015 campaign at UCLA.
- Stanley Kay