The Scotland international, 37, was an influential figure last season as the club secured promotion through the Championship play-offs.
Alexander has been rewarded with a new deal which will keep him at Turf Moor until 2010 following a string of good performances.
Alexander played 61 games for Burnley last season, culminating in the play-off final victory against Sheffield United at Wembley.
He weighed in with 11 goals as the club returned to the top flight for the first time in 33 years.
Alexander's new deal follows that of manager Owen Coyle, who
recently signed a two-year extension to his contract.
Burnley open their campaign on August 15 against Stoke.