The midfielder has agreed a three-year deal for an undisclosed fee and joined his new team-mates for training today at their pre-season base.
Hearts agreed a deal to sign Grant last week and, after finalising his release from Peterborough, he put pen to paper with the Edinburgh club. He joins Alan Forrest, Kye Rowles, Lewis Neilson and Alex Cochrane as new arrivals.
“I’m really pleased to get Jorge in as we continue to build our squad for a historic season,” manager Robbie Neilson told the club website.
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“He’s an experienced player who will bring dynamism and guile in the final third of the pitch and I’m really looking forward to working with him.
“The squad is starting to take shape but we’re not finished yet and I hope that in the weeks ahead we can continue to add quality to it.”
Joe Savage, Hearts’ sporting director, added: “We’re all delighted to be able to get Jorge over the line and have him join us out in Spain.
“He’s a really talented player and one we identified a while back as someone who could add value to the team, so to get him in a maroon shirt is great.
“Once again, our Board of Directors have backed us to get it right and I give them my thanks, as well as Jorge’s agent James, who has really played a massive part in helping to get this deal done.”