The transfer has opened the door for Andre Schurrle to join Chelsea with the South Korean acting as his replacement.
Son, 20, scored 12 goals in the Bundesliga last season and has signed on a five-year deal, much to the appreciation of the club's board.
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"Son fits in our requirements as a young, still very viable professional, with international standards.
"We are happy that he decided to join Bayer 04 Leverkusen as the club where he can best realise his own lofty goals.
"We have made it clear from the beginning that a transfer to Chelsea for Andre Schurrle is feasible only in conjunction with an adequate alternative.
"This alternative we have now got with Heung-Min Son. Thus, in our view there is nothing in the way of a transfer to England for Andre Schurrle."
Leverkusen sporting director Rudi Voller is also satisfied after the successful acquisition of the forward and hopes the signing can help the club progress in the future.
"Heung-Min Son is exactly the type of player we were looking for in our young team," he added.
"He is fast, agile, technically strong and a great finisher. Son is helping us to achieve our goals in Bundesliga, DFB Cup and Champions League."