Smith, a guitarist, is the son of the late musician Fred "Sonic" Smith and singer Patti Smith.
His exchange of vows with White was part of a double wedding with Jack Lawrence and Jo McCaughey, the rock group said.
The ceremony took place in Jack White's backyard in front a small party of friends and relatives last Friday.
Meg and Jack, who still perform together as The White Stripes, married in 1996 and divorced in 2000.
Lawrence is the bassist for White's other bands The Raconteurs and The Dead Weather.