These insects are actually called crane flies, and sorry-- they don't eat mosquitoes.
They also don't bite or sting but can be a nuisance pest for some. In reality, crane fly larvae are a pest of turfgrass.
The best way to deal with crane flies is prevention. Learn how to prevent crane flies in your home and landscape by reading the blogpost ‘Mosquito Hawks' in Your House? Or by visiting the UC IPM Crane Fly web page.