All passengers on board the Excel Airways flight disembarked and were safe, state police at the airport said on Friday.
Excel said the captain made the decision to land in Italy after a passenger found a note written on the back of an airsickness back that read: "There's a bomb on this aircraft."
Excel Airways official Jane Sebuliba called the landing "a precautionary diversion".
Italy's Air Force said it sent an F-16 to escort the plane to the airport.
The airline said all security checks where followed at London's Gatwick airport prior to its departure at 1045 GMT.
The plane, carrying 269 passengers and nine crew, was diverted to Brindisi three hours later.
Salvatore De Paolis, a border police officer at the Brindisi airport, said authorities searching the plane had recovered a handwritten note in English that said there was a bomb on the plane. De Paolis told Sky Tg 24 television news that the search was continuing.
Excel said the flight was expected to resume later on Friday.
The ENAV agency said the plane, a Boeing 767, was bound for Hurghada, Egypt. Located on Egypt's Red Sea coast, the resort is famous for snorkeling and is a prime destination for low-cost flights from Europe.
On Wednesday, a 59-year-old woman caused a security scare when she allegedly passed notes to crew members, urinated on the floor and made comments the crew believed were references to al-Qaida and the September 11, 2001, attacks on the London-to-Washington, DC, flight.
United 923, with 182 passengers and 12 crew members, was diverted to Boston and landed safely - with two fighter jets escorting it - after the pilot declared an emergency on board.