The cousins, who have won from neighbouring Amethi and Sultanpur constituencies in Uttar Pradesh, belong to Congress and BJP respectively.
Rahul was the first to take oath in Hindi in the name of God, followed by Varun.
After taking oath, Varun, while returning to his seat, greeted Congress President Sonia Gandhi with folded hands.
Varun forgot to sign the register after taking oath and was quickly reminded by Congress member K Suresh and Sonia to sign the register.
While Samajwadi Party chief Mulayam Singh Yadav had taken oath earlier in the day, other three party MPs -- his daughter-in-law Dimple and nephews Dharmendra and Akshay took oath later.
Akshay's father and Rajya Sabha SP member Ram Gopal Yadav watched his son take oath from the Speaker's gallery.
After taking oath, Akshay touched the feet of Dimple, wife of Uttar Pradeh Chief Minister Akhilesh Yadav.
Former UP Chief Minister and BJP leader Kalyan Singh's son Rajveer also took oath.