Tomlinson, 22, who is one of five members of the hugely successful boy band One Direction, announced the takeover together with former chairman John Ryan on Thursday.
Tomlinson is a Rovers fan and will share the ownership 50-50 with Ryan, who resigned as chairman in November after 15 years associated with the club.
"It's obviously unbelievable and an absolute honour as such a big Doncaster fan like myself," Tomlinson said.
"And to be involved with John who of course is very experienced and loved in Doncaster is great."
Doncaster were relegated from the Championship on the final day of last season but Tomlinson believes the club can climb up to the Premier League very soon.
"I think anything is possible and there's no point stumping your ambitions," he said.
"We are very ambitious and we're very enthusiastic - we're going to do the best we can and see where that takes us."