Centre Darren Yapp's shoulder injury has forced free-scoring fly-half Paul Warwick - who has amassed 105 points in eleven outings this season, including a magical 32 in the First Round Second Leg victory over Narbonne - to cover at outside centre with 35-year-old Elwood in at number 10.
Flanker Matt Lacey, who also has a shoulder strain, is replaced by Michael Swift, with prop Ray Hogan, hooker Bernard Jackman and right wing Ted Robinson all returning to the fold.
Elwood's involvement will see him in direct opposition with former Scotland international Gregor Townsend - with the two having played against each other as far back as Ireland's 6-all Five Nations draw with Scotland in 1994.
Coincidentally, Connacht supremo Bradley was Irish captain that day, and he rates Townsend as possibly Montpellier's biggest threat.
"Although Gregor is 31 now, I have always rated him highly," said the former scrum-half. "He pulls the strings for Montpellier and has a nice blend of kicking and passing in his game.
"We will be getting a better idea of them over the next few days, but they are a very competent side and strong maulers.
"It is important we make the most of our home advantage and get a sound start and the psychological edge for the second leg," added Bradley.
Elwood and Townsend also locked horns when a Warren Gatland-coached Connacht earned a brace of ground-breaking Challenge Cup Pool wins over Northampton (43-13 at home, 20-15 away) in 1997/98.
This afternoon's meeting kicks off at 2.30pm at the Sportsground in Galway.
(15) Matt Mostyn(14) Ted Robinson(13) Paul Warwick(12) James Downey(11) Conor McPhillips(10) Eric Elwood
Replacements:(16) John Fogarty(17) Dan McFarland(18) Peter Bracken(19) Pieter Myburgh(20) Brendan O'Connor(21) Conor O'Loughlin(22) Michael Walls