The Villa pair were handed shirt numbers six and eight respectively, with Elphick also being named the club's new captain.
Elphick and Tshibola are two of four new signings made by Villa boss Roberto di Matteo this summer, with the former joining from Premier League side Bournemouth and the latter arriving from Championship rivals Reading.
Captain at the Cherries until his move to Villa Park, Elphick had been touted as a leading candidate for the captaincy under the Italian manager as the club gear up for an arduous Championship campaign.
On Friday it was confirmed that the 28-year-old will be handed the armband for the relegated side, and he admitted on Twitter that it was a huge honour to be the man chosen to lead the Villans on the field.
Thank you for the messages huge honour— Tommy Elphick (@TommyElph4) August 5, 2016
Shortly after the announcement, he tweeted: "Thank you for the messages, huge honour".
Elphick has been handed the number six shirt, and both that and his selection as captain suggests he will be a key cornerstone of Di Matteo's defence this term.
Another new signing who has been handed a first-team number is Tshibola, who joined from the Royals earlier this summer.
The 21-year-old has been given the number eight shirt worn in recent years by such stars as last season's stand-out player Idrissa Gana Gueye and James Milner.
Tshibola could not hide his delight at being awarded the number eight, and voiced his pleasure on Instagram shortly after Elphick's tweet.
Whether or not that number will be mirrored by a starting role in the centre Villa's midfield this season remains to be seen, but Tshibola will hope to live up to his predecessor in the shirt.
Villa kick off their Championship campaign with a tricky trip to last season's play-off finalists Sheffield Wednesday on Sunday.