The former Great Britain international, 38, will enter his sixth consecutive campaign as No 2 and will continue to work under head coach Tony Smith.
Hodgson enjoyed an illustrious playing career, scoring 186 tries in 371 appearances for five Super League clubs. The Hull-born outside-back touched down on 34 occasions in Rovers colours and came out of retirement for a brief spell during the 2017 Championship campaign.
He is joined by Willie Poching on the backroom staff roster, who returns to the club following a three-year absence.
“I have been here a while now and to sign an extension for another year, and to be able to work under Tony and the staff that he has brought in too, is going to be great,” said Hodgson.
“For me personally I am always learning from everybody at the club. It is something that I pride myself on. I hope I can carry on learning throughout my career, and I have a great opportunity.”
Smith added: “Dave is well respected and is a very competent coach.”
Toronto Wolfpack have decided against taking any of their Super League matches to the continent in 2020.
The Canadian club have spoken publicly about taking top-flight fixtures to Copenhagen, Barcelona and Dublin and were last week offered the chance to stage a game in the Netherlands.
The Wolfpack will not play any home games until the middle of April because of the harsh Canadian winter which means moving three “home” matches.
But chairman Bob Hunter says there has not been enough time to put those plans in place.