The 21-year-old, who is battling for a spot in Germany's World Cup squad, opted to stay despite interest from some of Europe's top teams.
He has scored six times in the league and provided four assists this season and has grabbed a total of 24 goals in 126 Bundesliga matches since joining Leverkusen midway through the 2013-14 season.
"I see that something really big is growing here," Brandt, who has earned 14 caps with Germany, said in a statement.
"The recent contract extensions of Jonathan Tah and Lars Bender (both Germany internationals) have shown that. We want to win titles."
Leverkusen are fifth in the Bundesliga with six matches left in the campaign, with the top four teams qualifying for next season's Champions League.