Sinn Fein’s Philip McGuigan was also elected on the first count.
Mr Swann was Northern Ireland’s health minister during the Covid-19 pandemic.
He polled 9,530 first preference votes, narrowly ahead of Mr McGuigan on 9,348.
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TUV leader Jim Allister was just below the quota with 8,282 first-preference votes.
Robin Swann UUP 9,530 ELECTED
Philip McGuigan SF 9,348 ELECTED
Jim Allister TUV 8,282
Mervyn Storey DUP 6,747
Paul Frew DUP 6,242
Patricia O’Lynn All 4,810
Matthew Armstrong TUV 2,481
Eugene Reid SDLP 1,919
Bethany Ferris UUP 856
Paul Veronica Green 343
Laird Shingleton Ind 66