The 27-year-old Sandro has won three Serie A titles and three Italian Cups since joining from Porto in 2015, where he also won two league titles.
His five-year contract worth 26 million euros ($29 million) was due to expire in 2020.
"Today for me, my family and also for my teammates is a very happy day. To the fans I would like to say that I will always give my best, as I have done so far, and to keep improving," said the left-back.
"In the years that I've been here I learnt the mentality of the club and of my teammates. Here we always work to win and this will never change," said Sandro.
The Brazilian had been linked with a move away from Turin to an English Premier League club over the past two seasons.
"Power, control, technique and game vision. Alex Sandro has shown himself to be one of the most important elements of a team that has won three league and three Italian Cups since his arrival from Porto," Juventus said in a statement.
"Here's to continuing that commitment, going forwards to earn new victories and win more trophies!"