The minister announced his resignation on Saturday just as police fired tear gas to scatter young protesters in New Delhi, hours before their leaders were set to hold another round of talks with ministers.
"Considering the situation that has arisen at Jantar Mantar and across the country, so that anti-national forces do not take advantage of this situation ... I have sent my resignation letter to the prime minister," Pradhan wrote in a post on X.
"I deeply respect the aspirations, feelings, and legitimate expectations of the country's youth."
Cheers erupted among the thousands of protesters who have been rallying in central Delhi and elsewhere as the news spread.
"We have done it," said Abhijeet Dipke, founder of the Cockroach Janta Party that led the protests, to loud cheers at the Jantar Mantar protest site in New Delhi.
Youngsters at the site shouted "Jai Hind", a patriotic slogan meaning "Victory to India".
The protesters later agreed to end their demonstration, a spokesperson of the movement told reporters after talks with the government.
Thousands of supporters of India's youth-led "cockroach" movement had been protesting since June, but anger boiled over since police on Monday injured dozens of students, launching baton charges and firing tear gas to deter crowds of protesters marching on parliament.
The protests, led largely by young people and triggered by discontent over leaks of question papers for high-stakes entrance exams, reflect anger over job scarcity, corruption and government accountability.
Pradhan, 57, is a senior member of Modi's Bharatiya Janata Party and the son of a veteran BJP leader. A minister since Modi first took office in 2014, he has held several portfolios including petroleum and natural gas, and steel, before becoming education minister in 2021, and was even mentioned in the past as a potential BJP president.
After news of Pradhan's resignation, federal authorities restored access to the mobile internet around the protest site, after blocking it for most of the week.
"Young generation is here. This is win for the constitution," protester Tluanga Ralte said, walking with a copy of the Indian constitution at the protest site. "We are not a lazy generation."