Collins had been working as interim manager at Bootham Crescent since late August following the early season dismissal of former boss Martin Gray.
The 41-year-old had originally joined the Minstermen to work as youth team manager but has now been handed the reins of the first team after impressing during his two-month stint at the helm.
Collins has lost just one of his eight games in charge, winning four and drawing three.
A statement from York's board of directors said: "Over the past few weeks, Sam has displayed the ability to take the club forward and fully warrants this opportunity.
"This important decision was reached after conducting a lengthy interview process. There has been significant interest in our vacancy and the board has interviewed some high quality candidates.
"We firmly believe that Sam has all the necessary attributes to develop into a top young manager and the board will support his efforts in every way possible as he strives to lead the club to success this season."
Last month Collins told the Yorkshire Post that he would "love" to take charge on a full-time basis.
He said: “I’m probably getting to an age now where I’d like to have a crack at being manager of a club and this is a really good one to have the opportunity to do that at."
Collins' first game in charge as permanent manager will be Saturday's National League North trip to Southport.
The club have not announced the length of Collins' deal but confirmed that Stuart Parnaby has been made assistant manager on a permanent basis.