The left-back came close to joining Italian giants AC Milan back in January only for the move to collapse at the last minute when a medical picked up an issue with his heart.
Since then Robinson has been undergoing treatment for the issue – with the 22-year-old finally given the all-clear to return to training with Wigan last week.
“I would like to thank everyone who has supported me over the last few months – with a special thanks to club doctor Jonathan Tobin, the club’s medical staff and all of the team involved at the Liverpool Heart and Chest Hospital,” Robinson said.
“I can’t wait to get back to doing what I love. It has been a challenging time but I have good people around me. I am glad to be able to get back to training and have the opportunity to play for Wigan Athletic again.”
AC Milan were reportedly ready to pay £10million to sign Robinson earlier this year.
But it is now understood Albion are among the front-runners for his signature if they win promotion to the Premier League.
West Ham have also been linked with a move for the defender.
Head coach Slaven Bilic and technical director Luke Dowling have identified players depending on whether they are competing in the Premier League or Championship next season.
The Baggies are likely to be on the hunt for a new left-back this summer.
Kieran Gibbs, Conor Townsend and Nathan Ferguson have all been used in the role this season.
But Gibbs’ campaign has been blighted by injury, while Ferguson is expected to join Crystal Palace.