The Slovakian has signed a two-year deal at Tynecastle and becomes a permanent Hearts player after spending the last two years on loan at the Gorgie club.
"We are delighted everything is sorted out," manager Jim Jefferies told the club's official website.
"Since I came in he has impressed me and I think the club has three very good goalkeepers now.
"There is very little between them and they work hard with Arturas [Ramoska, goalkeeping coach] so it is very difficult to know who the number one is but Marian was the more favoured one last year.
"He had a bit of an injury problem and he's now had the game against Millwall so there's a couple of games to assess who will be the number one."