The Scotland pair missed the opening RaboDirect Pro12 defeat at Munster through injury but are back in the starting line-up for the visit of the Welsh side.
Walker will be making his debut following his summer move from Ospreys.
Solomons said: "I think this is a really good opportunity for Tim and Nikki to get involved.
"They're back to fitness, which is a big positive for us, and it's great to have them in the team.
"That said, I think that the lads have been playing well on the wings."
Edinburgh's injury list has not subsided any, however, as stand-off Piers Francis (ankle) and centre Ben Atiga (knee) have dropped out.
Harry Leonard comes in as number 10 while Dougie Fife moves to centre from the wing as Lee Jones, who scored a try in the 34-23 defeat by Munster, misses out.
In the pack, Georgia international Dimitri Basilaia starts his first match of the season in place of Sean Cox. Ross Ford takes over as captain.
New signing Wicus Blaauw is looking to make his debut from the bench while Newcastle Falcons and former Scotland under-20 centre Michael Tait, who is on trial with Edinburgh, is also included among the replacements.
The likes of Matt Scott (ankle), Ross Rennie (shoulder) and Greig Laidlaw (knee) remain on the sidelines.