The 20-year-old England under-21 international has previously impressed in temporary spells with Cheltenham and Lincoln.
Blues boss Danny Cowley said: “He’s one that we’ve been patiently waiting for and actually came very close to signing around this time last year.
“The timing wasn’t quite right on that occasion, but we’re absolutely delighted to have him with us now.
“Josh is a top young goalkeeper and we want to accelerate his progress. It’s a move that can work for everybody.
“He’s a great kid who’s extremely professional and hard-working, while staying focused on trying to get better every single day.
“Josh has brilliant loan experience already at Cheltenham and Lincoln. We think it’s a good time for him to come here.
“He will certainly provide a physical presence in the box and can command his area, but he’s all incredibly mobile.
“He’s an excellent shot stopper and is also very good with his feet, so he’s a really rounded goalkeeper.”
Griffiths has progressed through the West Brom academy after joining the club at the age of 10 and penned a new deal last summer.
He spent the whole of the 2020/21 campaign with Cheltenham, making 50 appearances and helping secure the League Two title.
That included an FA Cup outing against Manchester City, while his form with the Robins earned a ‘Young Player of the Season’ accolade from supporters.
Griffiths was then lent to Lincoln last term and featured on 35 occasions under former Blues boss Michael Appleton.
