The historic moment, streamed live by the Indian space agency, was watched by Indian Prime Minister Narendra Modi and millions around the world.
This was India's first successful lunar landing and paves the way for the country's ambitious space programme, including further, more complex missions to the Moon and beyond.
India is now the fourth country to softly land on the Moon, after the US, the former Soviet Union and China.
UAE President Sheikh Mohamed offered his congratulations to India on the milestone achievement.
"The successful lunar landing of India's Chandrayaan-3 spacecraft represents a significant leap for collective scientific progress," he wrote on social media.
"I extend my heartfelt congratulations to Prime Minister Narendra Modi and the people of India for this historic achievement in service of humankind."
Sheikh Mohammed bin Rashid, Vice President and Ruler of Dubai, also offered his best wishes to India on its successful Moon landing.
"Congratulations to our friends in India for the successful landing on the Moon," he said, writing on social media.
"Nations are built through perseverance, India continues to make history."
'Dawn of new India'
Mr Modi, who was speaking remotely from South Africa, said it signalled a new era for India.
"When we see such historic moments it makes us very proud. This is the dawn of new India," the Prime Minister said.
"Every person is celebrating. I am also celebrating with my family on this day.
"I congratulate every citizen, Isro [Indian Space Research Organisation] and the world with all of my heart."
More than 8 million people were watching Isro's live stream on YouTube, which beamed views of the lunar surface from Vikram's camera.
Isro's mission control erupted in applause when the craft safely touched the surface.
Race to the lunar south pole
Engineers will now spend the next few days monitoring the health of Vikram before a small rover, called Pragyan, is activated from inside of it.
Both will spend one lunar day, or 14 Earth days, studying the Moon's surface and taking images of the unexplored area.
The landing paves the way for the country to develop technology that could help in lunar mining.
The region is said to be rich with water ice that could be used to fuel spacecraft. It is also thought to hold other resources, such as metals and minerals.
Shri Charan Padala, principal analyst for the thematic intelligence team at GlobalData, said on Wednesday before the landing: "Chandrayaan-3, if successful in landing at the south pole, gives India a head start in developing the infrastructure and technology needed to mine these resources."
“However, formidable technological hurdles loom India’s lunar mining ambitions.
"One of the biggest challenges is the harsh environment of the Moon.
"The Moon is bombarded by radiation from the Sun and its surface is covered in dust that can be abrasive and corrosive.
"Designing space tech that can withstand these harsh conditions is a highly complex process."
India's space ambitions
The cost of the Chandrayaan-3 mission is 6.15 billion rupees ($74.2 million), while Russia's Luna-25 mission reportedly had a price tag of $200 million.
Luna-25 crashed on the lunar surface a few days after carrying out a manoeuvre which did not go as planned.
This was India's second attempt at a Moon landing. Its Vikram lander, part of the Chandrayaan-2 mission, previously crash-landed due to a software issue.
India is investing more in its space programme as it lines up more missions to the Moon and is preparing sending its first citizens to low-Earth orbit.
Isro is developing a capsule and rocket capable of sending astronauts to space.
It has already reached Mars orbit in 2014 – one of the cheapest Mars missions to date at a cost of $73 million.
India is leading the way for relatively low-cost space missions.