Arizona will receive $500,000 in international bonus pool money, according to MLB.com's Steve Gilbert.
Swihart was designated for assignment on Tuesday after appearing in 12 games for the Red Sox and hitting .231/.310/.385 in 26 at-bats. The Red Sox also have catchers Christian Vazquez and Sandy Leon on their active roster.
D-Backs general manager Mike Hazen said Swihart won't initially catch, and instead he'll move around the field, playing left field, right field, third base, and maybe some second base.
The 27-year-old offers Arizona that versatility after playing six positions during his five major-league seasons. The D-Backs already have three catchers - Carson Kelly, Caleb Joseph, and John Ryan Murphy - on their active roster, and Alex Avila on the 10-day injured list.
Swihart owns a career .255/.314/.365 slash line with nine home runs and 58 RBIs.
Wilson was the 20th-ranked prospect in Arizona's system, according to MLB Pipeline. The D-Backs drafted the 22-year-old in the second round in 2014. He hit .235/.350/.529 with two homers and seven RBIs in 34 at-bats for Double-A Jackson this season.