The new company will have its headquarters in the Chilean capital, Santiago.
Chile and Brazil have seen a massive increase in air travel but also recently tougher competition in the sector.
Once Brazil’s leading airline, Tam started to encounter losses as rivals began to offer cheaper tickets and better deals.
Latam’s chief executive, Enrique Cueto, told the Reuters news agency that the new carrier “will focus on Brazil and will introduce important changes in the local airline market”.
The combined revenues of Lan and Tam last year exceeded $13bn (£8.3bn). Their combined market value is second among the world’s airlines to Air China.
Analysts say both companies gain from the deal.