The 23-year-old joined the Hornets at the start of July but the two clubs were unable to agree a fee, prompting the west London meeting.
Watford were told they would have to pay an initial fee of £200,000 for the former Middlesbrough man's services, with incremental payments of £30,000 for every 15 appearances made up to a maximum of 75.
Should Watford gain promotion during the next three years, they will also have to pay the Cumbrians an extra £200,000, meaning they could end up paying £550,000.
"We feel we have acquired an excellent player in Danny Graham," Watford chief executive Julian Winter told his club's official website. "The fee represents good value for money."