The midfielder, who captained England U19s last season, will be reunited with his former Middlesbrough boss Tony Mowbray at the League One side after arriving from the Teesside outfit.
The Sky Blues manager handed the 19-year-old an opportunity in the first-team during his time at Boro, and Morris is hoping he can help him progress even further at the Ricoh Arena.
Morris, who has recovered from a stress fracture in his back, said: "I’ve had a frustrating time with my injury lately so I’m just glad to get back focusing on the football and I’m delighted to be here.
'He's got great potential and we're hoping we can help him realise it during his time with the club'
Tony Mowbray on Bryn Morris
"When I was 16, the manager had the faith in me then so I’m glad to be back working with him. He gave me my debut for Middlesbrough in The FA Cup and I’m really looking forward to getting started, I can’t wait," he told CCFC.co.uk.
"[Last season] I was at Burton for a month and while I didn’t play in my favoured position, I still enjoyed the experience. I played on the wing but I prefer a central role and like to go box-to-box.
"Either way, I’ll play where I’m told to, but the way Tony Mowbray spoke to me about it I’m really excited to kick on. I want to try and make my claim here and continue improving."
Morris has an impressive record within the national set-up, appearing for England's U16, U17, U18 and U19 sides and will be targeting a spot in this season's U20 squad.
Upon completing the signing, Mowbray said: "Bryn is player I've been aware of for a while due to his progression at my former club Middlesbrough; I handed him his debut when he was 16.
"He was able to gain some valuable experience last season at Burton and he showed he can cope with the physical demands of league football.
"We're delighted to be able to secure Bryn for the entire season as it gives us another option in central midfield, and he can also play centre-back.
"He's got great potential and we're hoping we can help him realise it during his time with the club."
Morris could make his debut for Coventry away at Wigan Athletic on Saturday, kicking-off 3pm.