FanDuel had to stop operating in the state in November after regulators ruled fantasy sports firms' activities amounted to illegal gambling.
The company also faced legal hurdles in a number of other states.
FanDuel later warned it may not be able to continue as a going concern due to legal obstacles in the US.
However, since January eight US states have passed laws "clarifying the legality" of fantasy sports, according to the company.
FanDuel, which was founded in Edinburgh in 2009, lays claim to six million registered users across the US and Canada. New York is one of its biggest markets.
Its technology platform allows sports fans to pick fantasy teams from real players, and follow their performances.
Chief executive Nigel Eccles welcomed the New York legislation, saying that sports fans in the state had sent more than 110,000 letters and made nearly 3,000 calls to lawmakers backing FanDuel's case.
He said: "Last fall, amidst national controversy, some pundits put fantasy sports on death watch.
"But when the calendar turned to 2016 and fantasy sports fans had the opportunity to be heard and legislators had the opportunity to act, the dynamic quickly shifted, and one by one states began to recognise this is a game loved by millions - millions who should be able to play and deserve the basic protections afforded to consumers in all major industries."
Earlier this week, FanDuel launched its first product in the UK - a new one-day fantasy football platform focusing on the English Premier League.
The move came after it struck a partnership deal with sports data provider Opta.
FanDuel has offices in Edinburgh and Glasgow but moved its headquarters to New York several years ago.
A Scottish tech firm is to resume its daily fantasy sports operations in New York, after a bill legalising the activity was signed into law.