ALEXANDRIA, Va.—Former Trump campaign chairman Paul Manafort was convicted Tuesday of eight charges related to tax and bank fraud, in the first trial to stem from special counsel Robert Mueller’s investigation.

The 12-member Virginia jury reached the guilty verdict on eight counts after four days of deliberations, but couldn’t agree on 10 additional counts of bank fraud and reporting violations. U.S. District Judge T.S. Ellis declared a mistrial on those counts.

Mr....