According to Fabrizio Romano, Bayer Leverkusen has accepted an offer of €20million including bonuses from Atlético Madrid.
It was already hinted early on Wednesday morning that a deal was nearing closer to completion between the clubs.
However, there is still some dispute over the exact transfer fee, which Sky Germany believes a figure of up to €25million is more accurate.
An agreement had already been reached between the left-back, who pushed for a return to club football in Spain, and Atlético Madrid.
Now all parties involved have given the go-ahead – after passing his medical, the 30-year-old will leave the Rhineland for Madrid.
Grimaldo is currently with the Spanish national team at the World Cup in the Americas, preparing for their clash with Uruguay.