The Finn will have to work under the same budget cuts which led to Calderwood's refusal to return following a short spell as boss at the end of last season.
Paatelainen was thrilled with his appointment. "I'm delighted to be manager of Kilmarnock Football Club," he said.
"I was desperate to get back into football and I look forward to it.
"I missed the training ground and the adrenaline."
Paatelainen added: "There is scope to improve the squad. Not too much, just a little bit.
"I hope to bring in a couple of players.
"I haven't spoken to any of the players and I don't intend to until July 5."