His time at Roma was much more impressive, yielding 34 goals in 83 appearances in all competitions, and Ince hailed some shrewd transfer dealing from Jurgen Klopp.
"I think it's a good bit of business," the former Reds midfielder told Sky Sports.
"I watched him play a lot this year at Roma. He scored a few goals – 15 or 16 this year I think he got, playing on the right wing. He scored all different types – long range, in the box.
"It didn't really work for him at Chelsea, he didn't get enough game time I don't think.
"But he's gone away, got his confidence back and he's come back to a great club like Liverpool and I think he'll be a great addition to Liverpool and I think the fans will enjoy seeing him play."