According to the Sabres' Twitter feed Thursday, Myers has agreed to terms. A news conference has been called for 2 p.m. ET Thursday.
Myers, the NHL's Calder Trophy winner as rookie of the year in 2009-10, will earn an average of about $5.5 million a season under the new deal, the source said.
Myers was set to become a restricted free agent July 1, 2012.
"We had two sides that wanted to stay together," Myers' agent, J.P. Barry, told the Buffalo News on Wednesday. "Tyler wanted to remain a Sabre, and having this done at an early stage was something that he wanted. He's happy that the club approached him about wanting to do this early."
Pierre LeBrun covers the NHL for ESPN.com.