The 19-year-old is an Iceland under-21 international and he has made five appearances for Albion's under-23 team this season.
He could make his Eastbourne Borough debut in their match at Truro City on Saturday.
Brighton under-23 coach Simon Rusk said: “Stefan has made good progress here, successfully moving up into the under-23 age group at the start of this season.
“We felt it was in the best interests of all concerned for him to go out on loan, and play in a very competitive National League South division.
“I’d like to wish Stefan all the very best for the rest of the season, and I’m sure this move will be very beneficial for his development.”
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