Campese, 30, arrived in the UK over the festive period to start a one-year contract with the Robins, where he will link up with his ex-Canberra team-mate Weyman.
He is one of three new half-backs in Chris Chester’s squad for 2015 – with Albert Kelly and Maurice Blair also joining from Gold Coast Titans, following the departures of Kris Keating and Travis Burns.
Weyman told the club’s official website: “He’s a really good bloke. He’s one of those fellas who’s been around a long time now and hopefully we can benefit from that experience.
“He’s played at the highest level for Australia and State of Origin and he can really lead you around the park well. He’s got a great kicking game that can get you out of trouble and he’s a great organiser.
“He’ll fit right in no worries at all. He’s a down-to-earth sort of character who everybody wants to play with and that’s the sort of player you want to have around.
“With Albert and Maurice coming in as well, I think they are three blokes who can really work well together.”
Hull KR start their pre-season campaign against Halifax at the KC Lightstream Stadium on Sunday (3pm).