The Chilean told the club's official website: "Jesus is a player I know well from La Liga and he is someone I have admired for a long time. He is quick, has excellent technique and I think the City fans will enjoy watching him play.
"I made Fernandinho one of the top priorities, he has impressed me on a number of occasions over the past few years and is another player I've taken a keen interest in.
"Both Jesus and Fernandinho add pace and skill to what is already a very talented and successful squad. I am looking forward to working with both our new signings and to working with the players who have already won a Premier League title together."
Pellegrini has previously managed Malaga, Real Madrid and Villarreal.