Are electronic signatures legally binding?

Yes.  Both US and European law have long recognised that electronic signatures are admissible in legal proceedings to determine the authenticity of any electronic communication in which they are incorporated.  Although a signature is commonly regarded as the writing by hand of one's full name or initials and surname to confirm one's willingness to be legally bound by a set of agreed terms, the courts have recognised that the essential characteristic of a signature is not what it looks like but the purpose it serves.  That is, a signature must demonstrate a signatory's authenticating intention (that the signatory intended to be bound by the terms of the document).  A person putting their thumb print on a document could be valid as a signature as it would be evidence that the person intended to be bound by that document.