Joshua, Grey's through-the-line agency, has been looking for a creative director since Ivan Palmer, who previously held the position, took on a strategic role as the executive partner.
Levy, who founded Spirit in 1998, has more than 20 years' experience at agencies including BMP DDB, WCRS, Ogilvy & Mather and Lowe Howard-Spink.
At Lowe, Levy art directed Smirnoff's "through the bottle cinema ad that won a gold Lion at Cannes.
"Joshua has recognised that the future is all about multi-discipline teams working together across the media mix. It's a vision that excites me and is what made its offer irresistible, Levy said.
Levy, who will run the 25-strong creative department, will report to Peter Thompson, Joshua's chief executive, and Nick Spindler, its managing director.
Spindler said: "What impressed us most was that Mitch is an above-the-line creative who has wholeheartedly been practising what we preach. He believes agencies can only continue to compete on a wider scale if they offer multi-discipline creativity."
Richard Hammond, Spirit's managing partner, said: "We wish Mitch well and thank him for supporting the agency for four-and-a-half years. He had an offer that he could not refuse and if you own your own business it has been a difficult 12 months."
Tony Ketley, Levy's deputy at Spirit, will become the acting creative director while the agency seeks a permanent replacement.
Hammond said: "We will replace him with someone from a high-profile background."