Neither Valentine nor the Red Sox would immediately confirm the agreement but local media, including ESPN where Valentine worked as a sports analyst, said the deal had been made.
Boston.com sports writer Nick Cafardo notes that with Bobby Valentine:
"The Sox stuck their necks out a little and thought outside the box. They are taking somewhat of a chance. They recognized that desperate times need desperate measures.
But in Valentine, they know they’re getting passion, one of the best in-game managers, and a guy who will speak his mind. Intellectually, he fits what they like."
ESPN said Valentine was currently in Japan and would return to America to be formally introduced as the new manager on Thursday.
He last managed in the Major Leagues at the Mets, leaving in 2002.
Valentine left his last management job at Japan's Chiba Lotte Marines in 2009 and began work as an expert television commentator before throwing his hat into the ring for the Red Sox job.
He takes over from Francona, who led the Red Sox to the World Series title in 2004 -- ending a championship drought dating back to 1918 - and again in 2007.
Leading the American League East by nine games at the start of the month, the Red Sox lost 20 of their last 27 games to miss out on the playoffs, earning the dubious distinction of the most awful final-month crash, a misery compounded by their status as pre-season favorites after a massive spending spree and a $161 million payroll.