Grabner scored a shorthanded goal that stood up as the winner in Saturday's 3-0 win over Los Angeles.
Grabner will make his Devils debut during Saturday night's home game against the Islanders, NHL.com reports.
The Rangers traded Grabner to the Devils in exchange for a second-round pick and prospect Igor Rykov on Thursday, Darren Dreger of TSN reports.
Grabner (coach's decision) will not be in the lineup Thursday against host Montreal amid rumors that he could be traded, Brett Cyrgalis of the New York Post reports.
Grabner scored two goals in a 6-3 loss to the Senators on Saturday.
Grabner (illness) will suit up for Sunday's tilt against Los Angeles, John Giannone of MSG Network reports.
Grabner was a late scratch for Saturday's game against the Avalanche due to the flu.
Grabner scored his 17th goal in Tuesday's 4-1 win over the Ducks.
Grabner had his team's first goal Wednesday in a 3-2 loss to Ottawa.
Grabner tallied his ninth goal in Sunday's 3-0 win over the Senators.