The 20-year-old scored three goals in 20 appearances in all competitions for Spurs last season after joining on loan in February.
Tel has signed a six-year deal with Tottenham for a transfer fee of around 35 million euros (US$40.4 million), according to German media reports.
Tel scored 16 goals for Bayern after signing as a teenager from Rennes.
Tottenham hired former Brentford boss Thomas Frank as their new manager earlier this week to replace the sacked Ange Postecoglou. (AFP)