The 27-year-old is the Tigers’ second capture of the summer following his exit from the Priestfield Stadium last month.
Eaves scored 21 goals in League One last term and he has already flown out to join up with the Tigers squad at their pre-season training camp in Marbella, with their number including free agent defender Ryan Tafazolli.
Liverpool-born Eaves, who spent a brief loan spell earlier in his career at Rotherham United, has signed a three-year deal with an option of a further year.
Head coach Grant McCann said: “Tom will be a great addition for us.
“He has got a different dynamic to what we have got and brings something different to our forward line.
“He comes here with a good pedigree. He was probably one of the best centre forwards in League One last season in terms of the goals he was scoring in a team that was not around the top end of the table, so we are really pleased to bring him here.”
Eaves, player of the year at Gillingham in 2018-19, joins QPR goalkeeper Matt Ingram in signing for the Tigers this summer.
Dale Tonge has signed a new deal at Barnsley and will continue to assist head coach Daniel Stendel next season.
The former Reds favourite, 34, moved up from the academy to assist Stendel alongside Christopher Stern following Andreas Winkler’s departure to Huddersfield Town in January.
Bolton-upon-Dearne raised Tonge has proved a popular figure with players during his time working alongside Stendel, playing his part in orchestrating the club’s strong second half to the campaign, which culminated in promotion back to the Championship at the first attempt at the end of last season.
The boyhood Reds fan spoke about his desire to continue his coaching education alongside Stendel at Oakwell and a deal has now been finalised for him to remain in his current position at the club.
On his new Oakwell deal, Tonge – promoted as a player to the second-tier in a joyous 2005-06 season under Andy Ritchie – said: “I am buzzing.
“I love the club, it was an honour to play for Barnsley and to still be involved now on the coaching staff is what I always wanted when I finished my playing days.
“We have felt a massive high from promotion and we have rightfully enjoyed it, now it is time to continue the progress and see where next season takes us,” he added.