Westmoreland, 19, underwent surgery to remove a cavernous malformation in his brain on March 16.
The surgery was performed by Dr. Robert Spetzler at St. Joseph's Hospital and Medical Center in Phoenix, and Westmoreland spent the initial part of his rehab there.
"After spending several days at that facility, Ryan made significant gains in his rehabilitation and was cleared to return to Boston to continue the recovery process," the Red Sox said in the release.
According to the Red Sox, Westmoreland, a native of Portsmouth, R.I., will continue to go through physical and occupational therapy at Spaulding, and the club added that he "has been making steady progress and is in great spirits."
Westmoreland's family asked the Red Sox to pass on their sincere appreciation for all the support and concern.
The family doesn't want to publicly speculate on what Ryan's recovery period will be like.
"We don't know, at this stage, what's going to happen," Ron Westmoreland, Ryan's father, told ESPNBoston.com. "The surgeon said it perfectly when he came out of the operating room. He said, 'First thing is his life, second thing is quality of life, and we'll deal with the rest after that.'
"Right now, he's trying to get back to a point where he can live a normal life. If baseball is in the cards, it's a bonus. Right now, we're just concentrating on quality of life."
Ryan Westmoreland visited the Boston clubhouse before Sunday night's game, speaking with manager Terry Francona, second baseman Dustin Pedroia, general manager Theo Epstein and several other people connected to the team. He then watched the game with his parents from Epstein's private box.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.