Shrews boss Graham Turner has finally got his man having been tracking Eaves for a while, with the 6ft 5in marksman bagging seven goals in 15 appearances during a loan spell with Bristol Rovers earlier this season.
"Tom is a player who we've been trying to get into the club for a while now and it's great news that Bolton have finally allowed him join us," Turner told Town's official website.
"Tom had options at a number of other sides, including ones higher up in our league, but Bolton and their director of football Lennie Lawrence thought the best option was for him to come here.
"He is a striker who scores goals and holds up play. We had him watched when Bolton reserves played Norwich on Monday and Tom scored the only goal of the game."
The 21-year-old Liverpudlian is available to make his debut in Saturday's home clash against Stevenage.