The 19-year-old striker was close to signing for Spurs in January, and has been monitored by a number of top clubs.
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The 26-year-old has signed a four-year deal with the La Liga outfit, with the fee reported as 1.2million euros (£1million).
Dembele, a French youth global struck up a formidable partnership with Scotland striker Ross McCormack last season and was linked with the likes of Arsenal, Chelsea, Liverpool, Juventus, Galatasaray and Stuttgart.
Scepovic, who was under contract until 2018, has been sold to Getafe after spending last season on loan there.
He scored six goals in 25 games in an underwhelming first season at Celtic Park after arriving from Sporting Gijon for £2.3m on transfer deadline day in August 2014.
Celtic assistant manager Chris Davies has not admitted or denied that the club are interested in signing striker Moussa Dembele.
Rodgers is looking to expand his striking options this summer, after Carlton Cole, Anthony Stokes and Stefan Scepovic all left Glasgow.
The Scottish champions are set to pay around £500,000 in a training compensation fee for the youngster, who has impressed many with his displays for Fulham in the Championship in recent seasons.
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“To be the first signing of Brendan Rodgers is something unreal for me”.
