After the acquisitions of Lewis Grabban and Kyle Lafferty this summer, Jerome has further bolstered Neil Adams' attacking options by signing a three-year deal.
"It's a massive club and from my point of view, where I am in my career, I just need to be playing regularly and Norwich have made me feel very welcome," Jerome told the club's official website.
"Once I spoke with the manager and a few other people here it was a no-brainer. The ambition of the club matches my ambition as a player and I'm looking forward to getting stuck into training and hopefully being involved at the weekend."
Jerome made 30 appearances in the Premier League last season but only one of them came for Stoke as he spent the majority of the campaign at Tony Pulis' Crystal Palace.
The former Birmingham and Cardiff striker, 27, scored just twice while with the Eagles, though.
Adams added: "He's someone I've been looking at for a long while and I'm delighted he became available to us. He gives us that brute strength as well as power, but he's got much more than that too.
"He works really hard for the team and he gives us that strength in depth that we'll need over a tough season."
Defender Cuellar also has joined the ranks at Norwich after agreeing a one-year contract with an option for a further 12 months.
“Carlos brings bags of experience as he’s played at the highest level in three countries. He can play as a centre-back and a right-back, and we’re brought him here to strengthen the options we have in defence,” said Adams.
“He’s a top quality player, so we welcome him into the squad and it will be great to have him available.”
The 32-year-old joins the Canaries after being released by Sunderland in June in which he spent six years in the Premier League, but the Spaniard reveals he is looking forward to life in the Championship.
“I’m so happy and so proud to join Norwich City. They’ve given me the opportunity to come here and I want to pay them back with performances on the pitch," Cuellar told the club's website.
“It is a big club but it is looking to get bigger and stronger and to move forward. I see the same mentality that I have of trying to improve all the time, so I think we’ll go hand in hand.
“I got the opportunity to see the Blackburn game live and the players did so well and played good football, scoring good goals so hopefully we can carry that on this season.”