Cuadrado was a free agent after leaving Juventus at the end of his contract last month.
The 35-year-old spent eight years with the Old Lady, winning five Serie A titles, four Coppa Italia trophies and two Italian Super Cups.
“I’m delighted and would like to thank God for this opportunity. For me, it’s an honour to be here at one of the biggest teams in Europe. I’m happy,” Cuadrado told the Inter website.
“I had many offers, but Italy is a second home for me. My family is very attached to this country, and there was the opportunity to stay here and play for a big team with a fantastic history.
“I chose Inter because we all know what they represent on a global level. The important thing is for my family and I to feel good. We had the opportunity to remain in a place that, for us, is home. It’ll definitely be the best choice.”
Cuadrado has also played in Serie A for Udinese, Lecce and Fiorentina.
He won the Premier League title with Chelsea during a short stint in the 2014/2015 season.
Cuadrado has been capped 115 times by the Colombia national team.
