India 'B' defeated Germany 3-1 in their final round match to end at third position.
Uzbekistan sprung a surprise by bagging the gold medal with a 2-1 win over the Netherlands ahead of a strong Armenian team, which beat Spain 2.5-1.5 in the final round, in the Open section.
The top-seeded India 'A' women's team crashed to a 1-3 defeat in the 11th and final round to USA to see it's gold medal hopes evaporate. The Koneru Humpy-led team finished third.
War-torn Ukraine won an emotional gold in the women's event, pipping Georgia to the top prize.
Uzbekistan beat the Netherlands in the final round thanks to Jakhongir Vakhidov's win on board 4. They edged out Armenia on the basis of a better tie-break score. The Uzbeks remained unbeaten through the 11 rounds and finished with 19 match points.
India 'B' ended up with 18 points for third place.
It was the second bronze medal for India in the Olympiad, replicating its feat in the 2014 edition.
The experienced B Adhiban, who was part of the team in 2014 added to his medal collection while it was the first for young stars D Gukesh, who was in spectacular form during the tournament, R Praggnanandhaa, Nihal Sarin and Raunak Sadhwani.
In the women's section, top player Koneru Humpy and R Vaishali drew their games against Gulrukhba Tokhirjonova and Irina Krush respectively. The defeats for Tania Sachdev at the hands of Carissa Yip and Bhakthi Kulkarni to Tatev Abrahamyan hurt the India 'A' team's chances of a gold medal.
Open: India's matches: India 'B' beat Germany 3-1 (D Gukesh drew with Vincent Keymer, Nihal Sarin beat Matthias Bluebaum, R Praggnanandhaa drew with Rasmus Svane, Raunak Sadhwani beat Liviu-Dieter Nispaenu).
India 'A' drew with USA 2-2 (P Harikrishna drew with Fabiano Caruana, Vidit Santosh Gujrathi drew with Wesley So, Arjun Erigaisi beat Linier Dominiguez Perez, S L Narayanan lost to Sam Shankland).
India 'C' drew with Kazakhstan 2-2 (Surya Shekhar Ganguly lost to Rinat Jumabayev, S P Sethuraman drew with Alisher Suleymenov, Karthikeyan Murali beat Arystanbek Urazayev, Abhimanyu Puranik drew with Kazybek Nogerbek).
Women: India 'A' lost to USA 1-3 (Koneru Humpy drew with Gulrukhba Tokhirjonova, R Vaishali drew with Irina Krush, Tania Sachdev lost to Carissa Yip, Bhakthi Kulkarni lost to Tatev Abrahamyan).
India 'C' lost to Kazakhstan 1.5-2/5 (Easha Karavade lost to Zhansaya Abdumalik, P V Nandhidhaa lost to Bibisara Assaubayeva, Varshini Sahiti drew with Xeniya Balabayeva, Pratyusha Bodda lost to Guliskhan Nakhbayeva).
India 'B' drew with Slovakia 2-2 (Vantika Agrawal drew with Zuzana Borosova, Padmini Rout lost to Eva Repkova, Mary Ann Gomes vs Zuzana Hagarova, Divya Deshmukh beat Svetlana Sucikova).
Other important results: Open: Armenia beat Spain 2.5-1.5, Uzbekistan beat the Netherlands 2.5-1.5.