Both deals begin on January 1 and run until the end of the current campaign.
Maffeo is joining Girona for the second time having played 13 games on loan there last season and Angelino is also embarking on his second loan switch away from City after he played 14 times for New York City FC in 2015.
Girona currently lie second in the Segunda Division, four points off leaders Levante.
Maffeo has played three times for the City first team under Pep Guardiola this season, including a man-of-the-match display in the EFL Cup defeat to Manchester United in October.
He also played two Champions League games, against Steaua Bucharest and Celtic, and impressed on both occasions.
The right-back joined City in 2013 and has progressed rapidly through the club’s academy system.
Angelino has made three appearances for the club - two this season in wins over Steaua and Swansea - and will be looking to use the move to Girona as a way of further impressing Guardiola and his backroom team.
Everyone at Manchester City would like to wish Pablo and Angelino well on their loan moves and we look forward to welcoming them back in the summer.