Farrell will speak to the media in a conference call on Friday.
"I am extremely thankful for the outpouring of support I have received from the Red Sox, my family, friends, and fans throughout this process," said Farrell in a statement. "I am also especially thankful for the talented doctors who cared for me in Detroit and here at MGH. I look forward to getting back to work and bringing another championship back to Boston."
President of baseball operations Dave Dombrowski announced on the final day of the regular season that Farrell would return to his post as manager in 2016 provided he made a full recovery.
Thursday's news was a significant step in that process.
"We are thrilled to hear the great news about John today," Dombrowski said. "Foremost, we are extremely happy for him and his family, knowing what he has gone through over the past two months. We all admire him for his strength and courage, and look forward to having him back as our manager."
Farrell's cancer was diagnosed during hernia surgery he underwent in Detroit on Aug. 10.
Four days later, after more definitive results from the doctors, Farrell announced his news and stepped down as manager for the remainder of the season. Torey Lovullo stepped in as interim manager and signed a two-year contract extension to stay on as bench coach.
"We can't wait to get him back," second baseman Dustin Pedroia said of Farrell on Oct. 4. "It's going to be good to have John back healthy and around the guys again. That's everyone's first concern, health. We want him to be back to normal and be fine. If he is, obviously he's going to be our manager."
Under Farrell, the Red Sox won a World Series in 2013.
The club finished in last place the last two seasons, but finished strong in 2015, helped by a strong nucleus of young players that leaves Farrell excited about the future.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.