The Board of Control for Cricket in India (BCCI), which met earlier in the day in Chennai, approved Pakistan's participation in the tournament which features leading domestic Twenty20 teams from around the world.
"We feel it's a significant and positive development," Pakistan Cricket Board chief operating officer, Subhan Ahmed, told AFP.
"We had been in touch with the BCCI over the participation of a Pakistan team and hope that this step could lead to a revival of Indo-Pak cricketing ties."
The news was also welcomed by Shoaib Malik, captain of Pakistan's Twenty20 champions Sialkot Stallions, who told AFP: "It's great news and I am happy to hear this."
"We eat the same food and wear same clothes and when we play cricket people of both countries come closer," he said.
The invite to the tournament, to be held in October in India, came a month after Pakistan President Asif Ali Zardari urged Indian Prime Minister Manmohan Singh to consider reviving cricket ties, during a private visit to New Delhi.
The Sialkot Stallions were meant to compete in the inaugural Champions League in 2009 but the plan fell through after the 2008 terror attacks in Mumbai, blamed on Pakistan-based militants, strained relations.
Malik, whose marriage to Indian tennis star Sania Mirza in 2010 bridged the two nations' bitter sporting and political divide, added: "I think its a small step towards reviving Indo-Pak cricket and I pray this continues at all level."
"We reach Delhi from Lahore in 45 minutes and it takes more time to fly to Karachi, so Pakistan and India are that close," he said, speaking from Dubai.
Malik led the last Pakistan team to India in 2007. India's last tour to Pakistan was in 2008 when they featured in the Asia Cup.
