Campbell and Bjorn carded 1-under-par 71s and Hedblom shot a 68.
Campbell's approach at the 411-yard par-4 18th came within a couple of inches of the hole.
Both Bjorn and Hedblom played decent approach shots. Bjorn, took his second runner-up spot in two weeks when his birdie try missed by inches. Hedblom missed left on his 15-foot birdie attempt.
"It has been a long time and it was hard," Campbell said after his sixth European Tour victory.
Campbell, 34, endured a miserable run in the United States, missing the cut in all nine events.
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