Sports wagering is not yet legal in either of the USA states, but both New Jersey and Pennsylvania are now eligible to regulate such services after last month's Supreme Court ruling on the matter.
Both the Senate and the General Assembly passed the bill after a round of lobbying during the morning and the early afternoon.
Some were hoping he'd do so Friday to get betting going immediately.
"He said he wants to act quickly, but the legislation will be subject to the same thorough review that all legislation sent to him for signature is subject to", his spokesman, Dan Bryan said Thursday.
Dermot Smurfit, chief executive of GAN, said: "Online sports betting "go-live" preparations are well advanced and we remain confident in launching as soon as reasonably possible in H2".
The last-minute amendment, however, could bypass that.
One state lawmaker notes that language that would have prohibited a casino or track from taking sports bets before the bill is signed was stripped from the bill before it was approved. It has said that it already has assigned 50 employees to Monmouth Park in anticipation of accepting sports bets.More news: Why Italy has closed its ports to a migrant rescue ship
Drazin told NJ Advance Media Thursday night he had not yet received the letter. "This is fast-developing". The bill would allow Atlantic City casinos and racetracks, including Monmouth, the Meadowlands and Freehold Raceway, to offer sports betting. Five pro and college sports leagues sued the state repeatedly since 2011 to stop the plans.
The state of New Jersey led the legal battle against various sports leagues that lasted six years before the Supreme Court's ruling on May 14, which deemed the federal ban on state-sponsored sports betting - via the Professional and Amateur Sports Protection Act of 1992 - to be unconstitutional.
You will be able to bet on all professional sports - everything from the victor down to prop best, like who catches the first touchdown. Churchill Downs also owns and operates twinspires.com, one of the leading account-wagering companies in the U.S. The partnership is expected to begin taking bets in the first quarter of 2019, the companies said at the time of the announcements.
The legislation passed on Thursday sets the tax rate for sports bets at casinos at 9.75 percent on gross revenue, with a portion of the money earmarked for the promotion of Atlantic City casinos.
Lawmakers who have long championed sports wagering were celebrating victory at long last in the state's quest to offer it. The bill also bans betting on high school games and on the increasingly popular electronic sports leagues.
If Monmouth Park or any casino does begin accepting bets on games, it will be without state regulation until Murphy signs the bill.
The bill also clears away obstacles for any of Atlantic City's casinos to offer sports betting, adding clauses to allow the Borgata, Caesars, Harrah's, Bally's and the Golden Nugget to offer sports bets despite ownership or partial ownership of professional sports teams.