Political parties cutting across ideological divide welcomed the development.
Shah said Modi's diplomatic efforts led to the United Nation's decision as he pitched for his "strong and decisive" leadership.
"That is why India needs a strong & decisive leader. Grateful to PM Narendra Modi and his diplomatic efforts that led to the UN designating Masood Azhar as a global terrorist. It was long over due. This also reflects PM Modi's commitment towards zero tolerance against terrorism," Shah tweeted.
BJP leaders asserted that the development shows that India is in safe hands.
"India stands vindicated. Masood Azhar is now a global terrorist. India is in safe hands. This marks a high point for the prime minister's foreign policy," senior BJP leader and Finance Minister Arun Jaitley said.
Calling it a "historic success" for India, the BJP used one of its Lok Sabha election slogans, 'Modi hai toh mumkin hai' (It is possible if Modi is there), as it reacted to what is being seen as a major diplomatic win for the country.
With the BJP making nationalism a key plank of its campaign, the party is set to highlight the development for political dividends in the election season.
Union minister Prakash Javadekar said it is a "big diplomatic victory" for India under Modi in the fight against terrorism and added that Pakistan now stands completely exposed.
Welcoming the move, the Jammu and Kashmir unit of the BJP said, "It is a great tribute to those killed in terror attacks in J&K and other parts of the country. This step will finish militancy in J&K."
Samajwadi Party president Akhilesh Yadav congratulated the Indian diplomatic corp for the tireless work that led to this "significant victory".
"We demand Pakistan immediately arrest him, freeze his assets and shutdown all organisations linked to him," he said.
In a huge diplomatic win for India, the United Nations on Wednesday designated Azhar as a "global terrorist" after China lifted its hold on a proposal to blacklist him.
Congress spokesperson Randeep Singh Surjewala said it was a welcome step but added that the opposition party was disappointed that the UN listing does not mention the Pulwama terror attack, which had killed 40 CRPF personnel, and has no reference to Jammu and Kashmir.
"Pakistan-based Masood Azhar's belated declaration as a global terrorist by UN is surely a welcome step. India's fight against terrorism is resolute. We are disappointed that UN listing doesn't mention Pulwama/J&K while listing Azhar's role in terrorist activities," he tweeted.
The Congress said it expected the Modi government to act with a "greater speed" in pursuing the case with China as several precious lives in terror attacks such as the one in Pulwama could have been avoided. The Modi government should now push for a declaration of bounty on Azhar's head as was ensured by the UPA in the case of Mumbai terror attack mastermind Hafiz Saeed, the Congress said.
Former Jammu and Kashmir chief minister Omar Abdullah alleged that the sacrifices of CRPF men were sold down the river for a symbolic win.
"No mention of terror in Kashmir & no mention of Pulwama. It's amazing how quickly the sacrifices of the CRPF men were sold down the river to get a symbolic win," he said.