Yes. According to a U.S. federal law called the Electronic Signatures in Global and National Commerce (ESIGN) Act, electronic signatures are as valid and enforceable as handwritten ones. The ESIGN act changed the status of all electronic signatures and made them as binding as their paper counterparts.
In addition to ESIGN, all of the U.S. states have adopted either the Uniform Electronic Transactions Act (UETA) or their own specific laws to establish the validity of electronic signatures for contracts in each state.
Finally, ESIGN provides that electronic signatures are legally enforceable for intrastate commerce and for commerce within those states that have not adopted UETA.
In summary, there are both federal and state laws firmly establishing that electronic signatures are as legally binding as a handwritten one.