A source told ESPN.com that the paperwork on the deal was being processed Friday morning. After Sessions signs, the Milwaukee Bucks will have seven days to match the offer, which they are not expected to do.
Sessions' name had been linked with the New York Knicks and Los Angeles Clippers throughout the summer. But New York was unwilling to guarantee more than one year -- which would tie up the Knicks' coveted cap space for the summer of 2010 free-agent market. And Los Angeles made a trade last month with Minnesota to acquire Sebastian Telfair as the backup to Baron Davis.
In Minneapolis, Sessions would compete for minutes with rookie Jonny Flynn of Syracuse, the sixth pick of the draft who was elevated to No. 1 on the Wolves' point guard depth chart after efforts to acquire Ricky Rubio's rights from the Spanish club DKV Joventut failed earlier this week.
That put the Timberwolves in the position of scrambling to find another playmaker, and the 23-year-old Sessions was the best option on the free-agent market after he and his agent, James "Chubby" Wells, decided weeks ago to hold off on committing to the Knicks in the hope a new opportunity would arise.
"We are excited about the opportunity to have Ramon Sessions on our team," Timberwolves president of basketball operations David Kahn said in a statement. "Ramon has the ability to play both guard positions, and thus will be able to complement the members of our current backcourt.
"At only 23, Ramon also has the potential to improve and fits our plan of building a young, up-tempo team with championship contending potential," Kahn said.
Unclear, though, is how the addition of Sessions for at least the next three seasons would impact Rubio's status with Minnesota.
The Wolves have been adamant that they will wait two years for Rubio if necessary. But Rubio's decision to stay in his native country when perennial Spanish club power Barcelona offered to pay his entire $5 million buyout with DJK Joventut, coupled with Sessions' looming arrival, only figures to encourage teams interested in Rubio -- such as the Knicks -- to try to pry him away from Minnesota via trade.
Matching the offer to Sessions, whose deal includes a player option for the fourth season, would put the Bucks over the luxury tax threshold, making it extremely unlikely the two-year veteran will return to Milwaukee.
Sessions averaged 12.4 points and 5.7 assists last season for the Bucks.
Chris Sheridan is a senior NBA writer for ESPN.com. ESPN.com senior NBA writer Marc Stein and The Associated Press contributed to this report.