The deal includes an option for UEFA Champions League semi-finalist Leipzig to purchase Angelino permanently on a deal until 2025.
Leipzig signed the left-back on loan in January and he scored one goal and supplied five assists in 18 appearances for the club.
"I'm very happy that I'm staying in Leipzig and that we can continue our journey together," said Angelino.
"The first six months with RBL were great; I had a lot of playing time from the start, I like the way the coach and the team approach the game. We also had a strong season in the Bundesliga and the Champions League.
"I'm looking forward to the future and many more successful moments."
Leipzig sporting director Markus Krosche said: "Angel needed little time to get used to our game and found his way around our approach right from the start.
"He played a strong second half of the season and helped us achieve our goals at the Champions League level.
"We are therefore very happy he will now wear the RB Leipzig jersey for at least one more season."
City first signed Angelino in 2012 but sold him to PSV following loan spells at New York City, Girona, Mallorca and NAC Breda.
It triggered a buy-back clause in the PSV deal in July 2019 and he made 12 appearances before being loaned out to Leipzig.