Jensen joins on a permanent deal after Deportivo La Coruna agreed a fee of around €6m with the German champions, seeing off competition from Italian side Lazio, who had proposed a loan with an obligation to buy that Bayern Munich rejected.
He spent the 2025-26 campaign on loan at Grasshopper, where he scored nine goals and provided six assists in 40 appearances as the Swiss side avoided relegation.
The Danish international made just one senior appearance for Bayern before his loan move, having progressed through the club's academy after joining from Midtjylland in 2022, and made his Bundesliga debut against Wolfsburg in May 2024. He has signed a contract with Deportivo running until 2031.
Jensen said he was delighted with life in the city and at the club, and had no hesitation in leaving Munich for A Coruna.
"When I got the call from Depor, I felt very happy. I had a great feeling from the very first moment, I think it's a good opportunity for me. I didn't have many doubts about signing," he said.
The winger made clear his focus is now on having a strong campaign with his new club, and believes his style of play suits Antonio Hidalgo's system well.
"Deportivo is a team that fits my style of play very well," he added.
Elsewhere, sporting director Fernando Soriano continues working to trim Deportivo's squad, looking to find loan destinations for several players including Charlie Patino.
Patino has offers from clubs in England's second tier and Poland's top flight, and is understood to be well down the road in negotiations.