The couple married in a lavish ceremony on Saturday (23.10.10) at the luxury Aman-i-Khas resort in Rajasthan, India, before jetting off on their honeymoon yesterday (25.10.10), and Russell hopes the couple will be able to make their way through the ancient Indian sex guide.
The comedian joked he would spend the next few days "taking Katy through the Kama Sutra".
After posting identical messages on their twitter saying: "WE DID!" the newlyweds boarded a private jet at Jaipur airport on Katy's 26th birthday yesterday and were believed to be en route to the Maldives.
A spokeswoman for Russell said: "They have gone off on their own. This is a special time for them now."
A friend of the pair added: "Where they're going is out of the way and they can just relax on the beach, enjoy each other's company and get massages with no other distractions."
Meanwhile, it has been reported the couple have run into trouble over their exit from the Aman-i-Khas resort after they reportedly left on a helicopter booked for airlifting a patient.
But Ravi Kumar, District Collector for the region of Sawai Madhopur, rubbished the claims, saying: "I gave permission for special landing of the helicopter to the hotel administration as they need to shift a patient to Jaipur. I am not concerned about who was travelling with the patient."
A complaint was also filed against six people including Katy and Russell for violating the Wildlife Protection Act through sound pollution caused by fire crackers and loud music during the marriage ceremony.