The 33-year-old's contract at Volkswagen Arena still had two years to run but he has opted to move to the Ligue 1 champions, agreeing a deal at Stade Louis II through to 2020.
The former Switzerland goalkeeper, who retired from international football in 2014, will compete with Danijel Subasic and Morgan De Sanctis for the number one shirt at Leonardo Jardim's title-holders.
"It's an honour to join AS Monaco, the reigning French champions," he said in a statement on the club website.
"I followed the team's results last year, they achieved great things. Obviously I've also followed Falcao's season and Kylian Mbappe's development. I can't wait to meet the squad. I'll be doing my best to bring my experience and everything I can to the team."
Benaglio, who made 14 league appearances last season, leaves Wolfsburg on good terms, stating his intention in a statement on the Bundesliga side's website to return to the club in the future.
"As much as I am looking forward to this new chapter in my career with AS Monaco, leaving here is very difficult for me," he said. "Wolfsburg and VfL have become the second home for my family and me. I am already looking forward to my return."
Wolfsburg sporting director Olaf Rebbe said: "What pleases us even more though is that we have basically agreed with Diego Benaglio that he will return to take a position at VfL Wolfsburg once he has finished his active playing career and that he will remain closely connected with us."