Nübel, 29, joined Bayern in the summer of 2020 but never established himself as a regular at the Allianz Arena. He has spent the past three seasons out on loan at Bundesliga side VfB Stuttgart, where he made 49 competitive appearances last season, 34 of them in the league.
Despite that consistent game time away from Munich, Bayern confirmed in late June — as first reported by Sky Germany — that they had decided to sell the goalkeeper this summer rather than extend his loan spell further.
With 40-year-old captain Manuel Neuer having signed a further one-year contract and Jonas Urbig continuing to establish himself as the club's long-term successor between the posts, Bayern's goalkeeping hierarchy left little room for Nübel to force his way back into first-team plans.
Nübel still has a contract at Bayern Munich running until the summer of 2029, giving the German club a strong negotiating position over any sale. According to the reported terms, Besiktas will pay €5m for the goalkeeper, with a further €5m in add-ons, taking the total package to €10m.
The German has three senior caps for his country and was part of Germany's squad at this summer's World Cup, though he did not feature during the tournament, with the national team's goalkeeping picture dominated by Neuer and Urbig throughout.
Earlier spells with Monaco and Schalke 04 also failed to deliver the sustained first-team run he will now be hoping to find in Istanbul, where regular football at a major club could finally give him the platform his early career once promised.
Nübel kept 38 clean sheets across his three seasons at Stuttgart, including 11 in the Bundesliga last term, numbers that will have appealed to Besiktas as they look to strengthen between the posts.