Veivers, 48, was sacked by the City Reds earlier this season following a turbulent off-season, and has previously served as assistant coach at Bradford and Wigan, ironically to new Reds coach Brian Noble.
The Australian, a full-back in his playing days, has been in this country since he left Queensland for St Helens back in 1984, spending 12 years at Knowsley Road and also playing for Huddersfield.
He said: "I’ve been away from the game for a few weeks, so I’m really looking forward to working with Brian and putting one over on England.
"We’ve named a strong squad, and part of my role will be to keep an eye on the players we’ve already named and those who are keen to break into it. There are plenty of outstanding players who haven’t been named and the door is still open."
McClennan last week named a 27-man squad, to be captained by Warrington's Brett Hodgson, for the game at the Halliwell Jones Stadium on Friday June 14.
With the glass ceiling to Super League being removed from next season, the path to the top flight opens up for Cumbria once again.
The Super League play-offs in their current form may attract some criticism, but they are keeping the season alive for several clubs in the bottom half.
The bonus point system, that has been in place in the Championships for the past eight seasons, is on the agenda for possible inclusion in Super League next year.
Bradford Bulls chairman Marc Green believes that the club needs to make more profitable use of its assets.