Left-back Fanai has been retained by the franchise while striker Udanta was signed from I-League club Bengaluru FC, according to a release.
Mizoram's Fanai made his debut with I-League side Shillong Lajong FC in 2012 and played for two seasons at the north east club.
He joined Bengaluru FC in the 2014-15 season, winning the Federation Cup and the I-League in successive seasons.
Twenty-year-old striker Udanta Singh has made four international appearances, his senior team debut was against Iran on March 24 in a World Cup qualifying match.
Commenting on the selection, Indranil Das Blah, CEO, Mumbai City FC said in the release, "We are elated to announce the signing of Fanai and Udanta. Fanai proved his mettle last season as well, and we're glad to have him back with us."
"Udanta had a great season in the I-League and is one of the most promising players in the country right now. His continued inclusion in the national squad at such a young age is a testament to that. We are sure they're going to play a big part in the upcoming season."
Fanai said, "It is great to be back in Mumbai. I hope I can play my part to give them a better season this time around."