A “large majority” of the more than 60,000 Uber Inc. drivers filing arbitration claims for employment misclassification will receive settlement payments as part of agreements reached by the company, Uber said in a regulatory filing May 9.

Thousands of drivers in two Uber lawsuits in California and Massachusetts against the company also agreed to dismiss their claims May 8, likely in exchange for multimillion-dollar settlements, according to court documents and agency filings.

The settlements and dismissals—which stem from drivers’ claims that Uber wrongly classified them as independent contractors rather than employees—remove the threat that the company could face tens of...