Taylor, the son of former Birmingham centre-back Martin, put pen to paper on a new three year deal at The Hawthorns earlier this month.
Tipped as a future Albion regular, the 19-year-old made his Championship debut at the end of last season.
Manager Steve Bruce has been contemplating whether to send Taylor out on loan or allow him to stay and compete for a first-team place.
But the boss has now allowed him to join Cheltenham on a season-long loan, with the manager believing Taylor needs to get more experience under his belt.
The move, though, does leave the Baggies with just three fit centre-backs as things stand.
They are Kyle Bartley, Dara O’Shea and Semi Ajayi – with Bartley having only just returned from injury. The Baggies allowed Cedric Kipre to join Cardiff on loan earlier this month.
Matt Clarke left the club at the end of last season following a successful loan, while Kean Bryan still isn’t ready to return to full training after suffering anterior cruciate ligament damage last November.
The Baggies, though, do have Jake Livermore, Darnell Furlong and Okay Yokuslu who have experience playing centre-half.
Bruce has also previously said he won’t rule out making a move to re-sign Clarke this summer.
“We’ve got to be respectful to Brighton and what they want,” Bruce said when asked about the defender earlier this month.
“They indicated that they wanted to see him in pre-season, to decide on what they wanted to do.
“We’re all spinning the plates. We’ve got to respect Brighton to see what they want.
“They’re only just back in training. We’ll see. But I’m not ruling that out.”