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.
In the United Kingdom, the equivalent legislation to the ESIGN Act in the United States was the Electronic Communications Act 2000.
In EU, eIDAS (EU regulation #910/2014) replacing the old Electronic Signatures Directive 1999/93/EC, is stating that qualified electronic signatures have the same legal status as a handwritten signature, and must not be rejected.