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Henrichs has made 15 appearances in all competitions since joining from Monaco, with his campaign hampered by injury issues.
However, the Germany international contributed his first goal involvement on Sunday (AEST), providing the assist as captain Marcel Sabitzer completed the scoring in second-placed Leipzig's 4-1 triumph at Werder Bremen.
The 24-year-old has signed a contract that runs through to 2025 after the purchase option was activated, reportedly at a cost of €15million.
"Since first coming to Leipzig, it’s been my goal to stay for the long term. I feel really good here and am pleased to be an RB Leipzig player for the coming years," Henrichs told Leipzig's website.
"The injuries I've suffered this season are completely behind me. Now I want to get back at it along with the rest of the team."
Leipzig's resounding triumph over Bremen allowed them to close the gap to leaders Bayern Munich, who were surprisingly held to a 1-1 draw by Union Berlin at the weekend.
Julian Nagelsmann's side trail the reigning league champions by five points with eight games remaining.
Henrichs previously played for Bayer Leverkusen before joining Monaco in 2018.