Green’s Dictionary of Slang

(US) an oral agreement or contract concluded without paperwork.

1992		W. Barrett Trump 284: [T]he patriarch arranged and attended meetings that produced [. . .] a handshake deal on a sale of the building to the tenants.
2000		P. Earley Super Casino 209: But from this point on, Schaeffer announced, the company wanted all of the details of its dealings with Wynn drawn up in a formal contract. There would be no more handshake deals.