The 28-year-old, who arrived at the Liberty Stadium in July 2012 from Rayo Vallecano, completed a medical with Rafael Benitez's side on Thursday morning.
Michu scored 22 goals in all competitions during his first season at Swansea but struggled to recapture that impressive form last term as injuries took their toll.
It is understood Swansea were keen to agree a permanent transfer for Michu, who managed only two goals in 15 Premier League starts in 2013/14.
The physical centre forward proved an instant hit after moving to the Liberty Stadium, scoring twice on his league debut in a 5-0 victory over Queens Park Rangers.
An excellent campaign resulted in Michu being voted Swansea player of the year by both his team-mates and the club's supporters in May 2013.
The striker was called up to the Spain squad for their FIFA World Cup™ qualifier against Belarus in October but ankle and knee problems hampered his contribution for club and country.
Benitez's side also lifted the Coppa Italia for the fifth time in the club's history and knocked Swansea out of the UEFA Europa League in their last 32 tie in February.