Currie, 22, is a former England U18 international who played for the Bath Academy until 2010, when he went onto play for Cornish Pirates. His performances brought him to the attention of the Worcester coaches who signed up the youngster last season.
Head Coach Richard Hill said: "It is good for them and we are going to try and get Ollie Hayes into a club too.
"These boys need to play and Leicester are a club that have done this very successfully. Dan Cole went out on loan and look at him now, Tom Youngs went out too. They go out for a few years then come back into the fold.
"There is no point having young lads on the bench or not in the match day squad. They have got to be playing for a good quality team and the likes of Leeds have good coaches and are a good club. They will do well there and develop."
Speaking about signing for Leeds Frost said: "I have been really impressed with the club since I arrived, we had our first training on Wednesday and myself and James were thrown in at the deep end with a tough session. The move to Leeds is really positive for me and hopefully I will be able to get more game time and it will be a fresh start. It is a young squad and I know Rory Clegg and Jacob Rowan from playing for England U18s so it has been easy to fit in. I have played in the Championship with Worcester and on loan with Coventry so I am looking forward to playing in the competition again and hopefully I will be selected this weekend and will get to play against some ex Worcester boys like Alex Crockett and Oliver Tomaszczyk in the Newcastle side."
Speaking about the move Currie added: "I am really pleased to have signed for Leeds, I have had my first training session today and there is good group of players here. I have played in the Championship before with Cornish Pirates so I know how tough the competition is. I think this move will be good for my career and my development and hopefully I will be able play regularly and help the club with their play-off ambitions."