Financial details of the deal were not disclosed by either club but British media reported that Bayern paid Spurs 3.5 million euros for the England international.
Dier, who had six months left on his Spurs deal, made over 300 appearances for the north London club since 2014 but has featured just four times since Ange Postecoglou took over as manager in June last year.
"He’s long been in our thinking for this transfer window. Eric will be a valuable part of our defence. His sporting abilities and international experience will help the team both on the pitch and in the changing room," Bayern said.
Dier was mostly used as a defensive midfielder under former Spurs boss Mauricio Pochettino and can also play as a centre-back.
His move to Bayern reunites him with former Spurs and England teammate Harry Kane, who has been in prolific form since joining the serial German champions.
Bayern are currently second in the Bundesliga, four points behind leaders Bayer Leverkusen, with a game in hand.
