While in Seattle fighting for the 20-year-old coffee chain Thursday, Dempsey said his investment group appears to have the winning bid.
The Seattle-based coffee chain filed for chapter 11 bankruptcy last fall after reporting $3.7 million in debts.
Tully's has dozens of coffee houses, including some in California.
Dempsey took to Twitter to share his excitement as the big news emerged.
"We met the green monster, looked her in the eye, and...SHE BLINKED!," Dempsey tweeted. "We got it! Thank you Seattle!"
A judge will have final say in a bankruptcy court hearing scheduled for Jan. 11 in Seattle.