The English side, who are coached by Spaniard Unai Emery, confirmed the news on their website on Thursday, while Ceballos said the presence of Emery at the club had been a factor in him accepting the move.
"I knew I had the confidence of the coach, which was very important for me from the start," he told the club's website.
"The coach was the turning point in terms of me joining this massive club. He's a Spanish coach and he knows me from my time at other clubs. He's a very tactical coach and I think that's going to really help me to perfect my positioning. I think we're both going to try our best to make me a better player," said Ceballos who did not have a good relationship with Real Madrid coach Zinedine Zidane.
Meanwhile, Emery celebrated the capture of the talented midfielder, who played a big role in the Spanish U-21 side's recent triumph in the recent European Championships.
"We're excited to see Dani join us. He is a talented player with big technical ability, creativity and precision," said Emery.