Two of India's leading construction firms have won bids to modernise Delhi and Mumbai (Bombay) airports, Civil Aviation Minister Praful Patel says.
The protestors threatened a strike if the government finalised the deal
GMR Industries and Frankfurt airport operator Fraport will modernise Delhi airport while the GVK group and its South African partner has won Mumbai.
Airport employees have announced they will go on strike across the country from Wednesday in protest.
The airports will be leased to the private companies as part of the deal.
They will be offered 74% stakes in the airports while the state-controlled Airports Authority of India will retain a 26% stake.
But the plan is bitterly opposed by trade unions and the government's communist allies who say the move will lead to job cuts.
The deal has still to be approved by the cabinet.
Heavy security was in place outside the civil aviation ministry before the bids were opened.
GMR-Fraport and GVK-ACSA (Airports Company of South Africa) outbid rivals Reliance and ASA Mexico, India's DS Construction and its partner Munich Airport and Australia's Macquarie group with partner Aeroports de Paris.
Hundreds of airport workers staged protests outside major airports including Delhi, Mumbai and Calcutta.
Employees of the state-controlled Airports Authority of India (AAI) announced they would strike in protest at the government's decision.
"More than 20,000 employees of AAI... have decided to go on a strike from 1000 Wednesday onwards," union leader MK Pandhe told the BBC.
The BBC's Nagendar Sharma in Delhi says the strike could severely affect air services and that a compromise between the two sides looks unlikely at the moment.
The aviation minister sought to allay workers' fears.
"The government has mandated that all the employees will be retained for the first three years," Mr Patel told journalists.
India's airports have been unable to match the growth in Indian aviation.
India recorded a 25% growth in air passenger traffic in the past year alone on the back of a booming economy and lower fares.
But poor infrastructure has led to delayed flights and logjams at the airports which are running out of space to handle the increase in passenger loads and aircraft movements.
India began to open up its domestic airline market - previously dominated by state-run carrier Indian Airlines - in the 1990s.