Lyburd-Hines, 21, began his career in Nottingham Forest's academy.
He joined Hereford in August 2021 following his subsequent released from the now-Premier League side before a move to Chippenham Town followed in April 2022.
The young shot-stopper enjoyed time with Lincoln United last season as they were relegated from the Pitching In NPL East Division following an inter-step play-off against Avro.
Lyburd-Hines will provide competition for Ghanaian international Felix 'The Cat' Annan, whose arrival at the Millers was confirmed last month.
Manager Tommy Brookbanks said: He has impressed us pre season and will challenge Felix for the number one spot.
"I would personally, on behalf of the club, like to thank Sam Wynch for getting this deal over the line.”