Tomas, 19, arrives on a loan deal until 2023 which can then be made permanent. He won the Portuguese league with Sporting last season and has also played Champions League football.
"We've been following Tiago's development for a long time. He brings a lot of qualities that will give us more options in attacking areas," Stuttgart sports director Sven Mislintat said.
Tomas said: ""I'm very happy to be here. VfB are a club with great history – one of the biggest in Germany. The Bundesliga is a very demanding league and I'll try to do my best to help my new team."
Stuttgart are second-last in the Bundesliga and host mid-table Eintracht Frankfurt after the international break on Saturday.
