The 22-year-old has replaced injured Jamie George in the squad for the Six Nations clash with Wales.
"I think he's exactly the right selection for the senior squad now that he's got through his injuries and is up and fit," Baxter told BBC Sport.
"It's disappointing for Jamie that Luke's opportunity has come off the back of someone else's injury, a lot of breaks in all sports happen like that."
Cowan-Dickie missed the early part of this season after breaking his thumb, and is in line to win his second cap should he replace captain Dylan Hartley at Twickenham on Saturday.
He was part of the England team that won the Junior World Cup in 2013 and was one of the final players to be cut from Stuart Lancaster's squad for last year's World Cup.
"To win an international cap or be picked in the senior squad you have to be a good player, but you have to work extremely hard as well and Luke's done that," added Baxter.
"He's had to be patient through a couple of significant injuries and despite that, he's got his head down and is improving as a professional player all the time.
"He's still improving as a hooker as well. He's still played relatively few top-flight games as a hooker.
"His conversion from loose-head has not been very long and he's doing a remarkably good job and he'll keep getting better."
Exeter boss Rob Baxter has backed Luke Cowan-Dickie to impress for England.