"We had a son on Dec. 26, and he was born with multiple issues that we confronted and had to deal with as we were moving through the last couple of months at Mass General," Hill told reporters in Fort Myers, Fla. "Unfortunately, he succumbed and he has passed. He taught us a lot of things, and unfortunately things didn't work out.
"My wife has been extremely strong. Our son, who is 2 1/2, is with us here down in Florida, so we are going to enjoy our time here and obviously make the most of the opportunity that's here to present itself to play baseball."
Hill hopes that the normalcy of being back in uniform might at least ease some of the pain he is going though.
"I'm absolutely excited to be here and be playing baseball again, to get back into the normalcy of my profession and to be around a great group of guys," said Hill. "Just to take that next step, a one day at a time approach. That's where we're at. Just really enjoy every day."
"Just reading his comments this morning, I know he's happy to be back, in spite of everything that's gone on," manager John Farrell said in Jupiter, Fla., before the Red Sox's game against the Marlins. "He can get back to doing what he loves to do, and that's to go out and compete."
Farrell added that Hill is probably going to need to throw "a few" bullpen sessions and then will progress from there.
A native of Milton, Mass., Hill has always maintained residence in the Boston area. He pitched for the Red Sox from 2010-12 before spending last season with the Cleveland Indians.
"Fortunately I had the opportunity to come back," Hill said. "The Red Sox have been tremendous with this whole part of our life."
The Red Sox have a crowded stable of lefty relievers, including Andrew Miller, Craig Breslow and Chris Capuano. But the 33-year-old Hill is taking a positive outlook as he starts his Spring Training.
"I fully feel that the opportunity is here," Hill said. "I think that was also with a blend of the opportunity that is here and obviously with our family situation that we had. ... With the opportunity that is here, I'll make the most of it and do everything I can on a daily basis to perform."