Sevilla announced the agreement for the 25-year-old, subject to a medical, on their website on Tuesday. Local media reported the fee at around 5 million euros.
Alexis, who is set to sign a five-year contract, joined Valencia from Getafe in 2007 but never established a regular place.
Sevilla said on Sunday they had agreed to sell France defender Squillaci to Arsenal subject to a medical.
Sevilla host Portugal's Braga in the second leg of a Champions League play-off on Tuesday, needing to overturn a 1-0 deficit.
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