Some informal way of saying "approve" would be best here:

See meaning "D"

Ramdon House

28. sign off,
a. to withdraw, as from some responsibility or connection.
b. to cease radio or television broadcasting, esp. at the end of the day.
c. Informal. to become silent: He had exhausted conversation topics and signed off.
d. to indicate one's approval explicitly if not formally: The president is expected to sign off on the new agreement.