Yes. Documents signed with swipesign are legally binding in the EU under eIDAS, and in the US under the E-SIGN Act and UETA.
That's the short answer, and usually it's the whole answer. The rest of this matters when someone disputes the signature.
What makes a signature hold up
Courts don't ask whether a signature was electronic. They ask three things. Can you show who signed? Can you show they meant to sign? Can you show the document hasn't changed since?
Answer all three and the signature is hard to argue with. Answer none and you've got a picture of a name.
That's why swipesign only issues Advanced (AES) and Qualified (QES) signatures. Both seal the document so later edits show up, and both identify the signer: though to very different standards. AES does it indirectly, through the email address and a phone number; QES does it through a qualified provider that checks an ID document. See AES and QES explained.
Valid is not the same as unchallengeable
A Qualified Electronic Signature has a specific status in EU law: it's legally equivalent to a handwritten signature, and it flips the burden of proof. Dispute a QES and you have to prove it wasn't you: rather than the other side having to prove it was.
AES doesn't flip anything, but it's still admissible and still evidenced. For everyday business documents it's normally the right call. For anything where losing an argument would be expensive, use QES.
What you can actually produce
Every signed document comes with an audit trail: who opened it, when, how their identity was checked, when they signed. The signature carries a certificate from a qualified trust service provider, and anyone can validate it without going through us, including after you stop being a customer. See What is in the audit trail and how to verify it.