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.
Four Super League players have been charged by the match review panel, including two from Leeds.
A record crowd of 15,912 attended the two days of Championship and League 1 action at the Summer Bash at Bloomfield Road.
BARLA Lions emerged triumphant over the Jamaica Hurricanes over the weekend.
Llanelli hosted a festival of 'Origin' fixtures for the Welsh community game on Saturday, with four intensely competitive clashes taking place at different age group levels.
Wigan have stated that one of their players may face disciplinary action over an incident in the town.