Eurosport - Anton Rodgers was previously with Chelsea's academy
The son of Liverpool manager Brendan will help the Grecians' promotion bid as he seeks regular first-team football.
Rodgers, 20, has made one senior appearance for the Seagulls, coming on as a substitute in the club's 1-1 draw against non-league side Wrexham in the FA Cup third round.
He could make his debut for his new side against Exeter's promotion rivals Rotherham at the weekend.
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