Mr Picon will replace outgoing global co-chairman Sir Nigel Knowles on 1 May.
Mr Picon joined the firm as country managing partner for Spain in 2006 from Squire, Sanders & Dempsey.
In 2007, he became international group head for corporate and in 2012 he joined the executive.
He was most recently appointed as joint managing director for Europe and the Middle East in 2014. He is also co-chair of the firm's Latin American practice alongside Bob Gruendel.
"I am absolutely delighted to be appointed,” said Mr Picon.
“The firm has an incredible momentum and I believe together, Simon and I, alongside Roger Meltzer and Jay Rains, will guide the firm into the next stage of its development."
Sir Knowles said the firm would be under the leadership of a new generation from May this year.
"I know that Juan and Simon make an excellent team and will be able to achieve great things for the firm," he said.