The 22-year-old is highly-regarded at the Bernabeu and helped the Spain Under-21 side to the Euro 2019 title earlier in the summer.
But with competition for places high in the Spanish capital the Gunners have moved in to secure an important addition for manager Unai Emery.
He will wear the number eight jersey most recently worn by Aaron Ramsey who joined Juventus on a free transfer at the end of last season.
Ceballos is likely to be joined by William Saliba with the 18-year-old defender set to join permanently before returning to St Etienne on loan.
With two bids for Celtic full-back Kieran Tierney turned down and a move for Crystal Palace's Wilfried Zaha seemingly dead in the water, Arsenal fans will be pleased to see further arrivals with teenage striker Gabriel Martinelli the only summer addition up to now.
Manager Emery is delighted to get his man.
“We’re excited to see Dani join us. He is a talented player with big technical ability, creativity and precision.”
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