McCourt, 30, has signed a one-year deal with the Skybet Championship outfit following a short trial period, with the option of a further season included.
The player left Barnsley during the summer and could make his Brighton debut against Bolton this weekend.
"Paddy is a player who sees the right passes, at the right time, and I hope he can help us in terms of creativity going forward," said Sami Hyypia, Brighton's manager.
Fenlon, having previously had McCourt on trial with Hibs, was keen to acquire his services but could not attract him to the Tallaght Stadium.
McCourt, who played 89 times for Celtic in five years, is also thought to have considered interest from from the USA and Qatar.
Peterhead, meanwhile, have signed former Dundee United midfielder Mark Millar. The player, who started his career with Celtic is eligible to play in tomorrow's away game against Airdrie.