The right-back, 20, left League Two Wimbledon this summer after making 41 appearances last season.
Fenlon, who rejected a new deal at Kingsmeadow last month, said on his Twitter account: “Glad to sign for Ross County. It’s a new challenge, can’t wait to start.”
Dons manager Neil Ardley said on the club's website following the player's departure in June that they could not afford to offer him improved terms.
He said: "Jim had an option on his contract, which would have taken him up amongst the highest earners at the club.
“This was an option that we felt we could not take up considering his form and attitude during the past 12 months.
"As with all Football League contracts, the club has to offer at least the same terms as the player was on to retain compensation rights. However, with our budget that was a step too far for us.
"We offered Jim a slightly reduced offer in the hope that we would be able to add the attitude required to his ability. But we have not been given that chance and we therefore wish Jim all the best for the future."
Fenlon would be County manager Derek Adams' eighth summer signing and would join Dutchman Jordi Balk, Belgian Tim Dreesen and England’s Ben Frempah at Victoria Park, if a move were to materialise.