The striker was injured in last month's 1-1 draw at Huddersfield but played in Leicester's next two matches with the help of pain-killing injections.
"Jamie had injections right after the Bournemouth game and he has fully recovered now", said Shakespeare. There's no ill effects'.
The 30-year-old has been Leicester's top scorer in the past two seasons and has already found the net five times in seven games despite Leicester's slow start to the campaign.
"It is always a odd week worldwide week but playing Monday has helped us this time in terms of getting everyone back and getting a clean bill of health", Shakespeare told club website.
The Foxes have only won one of their opening seven Premier League games to date this term, although they have faced hard fixtures against the likes of Arsenal, Manchester United and Chelsea. The midfielder appeared to injure his hamstring whilst playing for Nigeria, but the manager confirmed that he's ready to play, as is Chilwell, who missed out on worldwide duty with England's Under-21s having suffered a knock.
'There was a scare about Ndidi, but it was only cramp. He's fine so there's no problems there'.
West Brom will head into the match without a win in any of their last six matches in all competitions, with their back-to-back league victories at the beginning of the season starting to look like a distant memory.