Spurs entered talks with the 19-year-old last week after an agreement with the German Bundesliga club had been struck for a deal in the region of 60 million euros ($A100 million).
However, negotiations stalled on Friday with Arsenal, Chelsea and Manchester United also interested in the France U21 international, but he performed a U-turn over the weekend and has been persuaded by Tottenham boss Ange Postecoglou to join the club for the second half of the season.
Tel's loan deal does include the option for Spurs to make the transfer permanent in the summer.
It is a timely boost for Postecoglou, who has faced mounting external pressure but watched his depleted team make it three wins from their last four matches with a 2-0 victory over Brentford on Sunday.
He's here. Tel a friend 🗣� — Tottenham Hotspur (@SpursOfficial) pic.twitter.com/b9ELdatWarFebruary 3, 2025
The addition of centre-back Kevin Danso from Lens was confirmed on Sunday as Tottenham look to salvage their campaign with the prospect of trophy success still possible.
They face a crucial week with a trip to Liverpool on Thursday to determine who qualifies for next month's League Cup final at Wembley Stadium and an FA Cup fourth-round tie with Aston Villa three days later.
Postecoglou could have Tel available for both fixtures if he receives international clearance and a work permit in time.
Tel signed for Bayern in 2022 from Rennes and broke records shortly after his big-money transfer with goals against Viktoria Koln and Stuttgart respectively making him the youngest scorer for the club and the youngest scorer in the Bundesliga.
The forward struck six times across 28 appearances during his debut 2022-23 season and 10 in 41 fixtures last campaign, but he has fallen out of favour under Vincent Kompany.
After only four starts this term, the door was opened to move on and Tottenham have won the race for his signature.
Manchester City completed the signing of FC Porto midfielder Nico Gonzalez until 2029 for 60 million euros.
The Premier League champions forked out a combined $A246 million to bring in Eintracht Frankfurt forward Omar Marmoush, Palmeiras defender Vitor Reis and Lens centre-back Abdukodir Khusanov in January.
"This is the perfect opportunity for me at this stage of my career," Spain U21 international Gonzalez said.
"I am 23 and I want to test myself in England. There's no better club than Manchester City for me to do that.
"Look at the squad they have here, it's unbelievable, full of world-class players. There isn't a footballer in the world who would not want to be part of this set up.
"I know the reputation Pep has and I cannot wait to work with him. In fact, I am honoured he wants me to play in his team."
Elsewhere, Aston Villa signed Spanish attacking midfielder Marco Asensio on loan from PSG, while Evan Ferguson has teamed back up with former Brighton & Hove Albion boss Graham Potter, on loan at West Ham, both until the end of the season.
Chelsea have allowed 21-year-old midfielder Carney Chukwuemeka to join Borussia Dortmund on loan, Newcastle United defender Lloyd Kelly moved on loan to Juventus, while Wolves left it late to announce the arrival of defender Nasser Djiga from Red Star Belgrade on a deal which runs until 2030 with the option of another 12 months.
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