signed
v.v. to write your name on a document to show that you agree with it or that you wrote it. You often do this for letters, contracts, or bank forms.
v. to write one's signature on a document as a token of consent, obligation, or receipt. Transitive when taking a document as an object; also used intransitively.
Please sign your name at the bottom of the page.
The athlete signed a three-year contract with the team after passing a medical examination.
Before the digital era, authors signed every copy of their limited edition books by hand to guarantee their authenticity to collectors.
The verb is transitive and takes a direct object, such as a document or a name.
I signed on the contractI signed the contractWhen referring to a document, the verb is transitive and does not require a preposition.