Pakistan had earlier invited External Affairs Minister Sushma Swaraj for the ceremony.
Swaraj, who was unable to travel to Kartarpur Sahib due to prior commitments, had said India would be represented by Badal and Puri.
Talking to reporters at Attari in Amritsar, Badal said it was an emotional moment for her to visit the historic Kartarpur Sahib gurdwara in Pakistan.
Puri said he was privileged and blessed to get an opportunity to pay obeisance at the shrine.
Pakistan had also invited Punjab Chief Minister Captain Amarinder Singh and his cabinet colleague Navjot Singh Sidhu.
While Singh declined to attend the event, citing continued terrorist attacks in his state and killings of Indian soldiers by Pakistan's armed forces, Sidhu left for Pakistan on Tuesday.
Congress MP from Amritsar Gurjeet Singh Aujla and Shiromani Gurdwara Parbandhak Committee (SGPC) chief Gobind Singh Longowal have already reached Pakistan for the ceremony.
The corridor will facilitate easy passage for Sikh pilgrims to the historic Gurdwara Darbar Sahib Kartarpur in Pakistan.
It has been a long-pending demand of the Sikh community.
Kartarpur is located in Shakargarh in Narowal district of Pakistan's Punjab. Guru Nanak Dev, the founder of Sikhism, had spent more than 18 years of his life there.
The Kartarpur Sahib Gurdwara is located on the banks of the Ravi river, about three-four kilometres from the border in Pakistan.