The official announcement will come at a Thursday news conference. The new deal will pay Doan $4.55 million a season.
"From the outset, both sides have always said that our first priority is to remain together," Coyotes GM Mike Barnett told The Canadian Press on Wednesday. "The negotiations have been respectful and most recently have been productive."
Coyotes CEO Jeff Shumway, GM Mike Barnett and Doan's agent J.P. Barry made significant progress during contract talks Monday and Tuesday.
"We have been working on an extension for Shane since last September," Barry told CP on Wednesday. "In the last three days we have had face-to-face meetings with the ownership and management team of the Coyotes and we have agreed upon the framework of a long-term extension.
"It was Shane's desire to remain a Coyote for life so he is very pleased with the progress we have made. We expect to finalize our agreement shortly."
Doan, 30, is earning $3.38 million this season and was slated to be an unrestricted free agent July 1.
The native of Halkirk, Alta., has played his entire 11-year NHL career with the Winnipeg/Phoenix organization. He leads the Coyotes with 19 goals in 48 games this season, while adding 16 assists. He had a career-high 30 goals in 82 games last season.