The Prince will on Friday represent the Queen as Head of the Commonwealth at the opening ceremony, and will host other Commonwealth events, including a reception for business leaders and a dinner for heads of government.
Pakistan Prime Minister Nawaz Sharif too arrived here Thursday.
Amid a boycott by the prime ministers of Canada and Mauritius who have voiced concerns over human rights violations in Sri Lanka, and the absence of Indian Prime Minister Manmohan Singh, Rajapaksa said he was willing to "look into" human rights issues surrounding the war that crushed the Tamil Tigers in 2009.
The Prince will represent the Queen as Head of the Commonwealth at the ceremony.
Rajapaksa told a media conference that ending the three decade old war had proved immensely beneficial for Sri Lanka, reports Xinhua.
He insisted that his government had established adequate systems to tackle rights issues.
"We have suffered for the last 30 years. All people suffered, but no one is getting killed in Sri Lanka now."
Rajapaksa said he would be willing to impartially investigate allegations made against the military.
"We are ready to look into it... We have nothing to hide."
The spotlight on Sri Lanka's human rights situation intensified after Rajapaksa was given chairmanship of the Commonwealth till the end of 2014.
Canadian Prime Minister Stephen Harper led the international protest over Sri Lanka's rights record by boycotting CHOGM. His Indian and Mauritius counterparts also bowed out from the leaders' summit.
British Prime Minister David Cameron has vowed to raise accountability issues with Rajapaksa.
The main opposition United National Party (UNP) said it was boycotting the Commonwealth summit after a pro-government group attacked the UNP headquarters on the outskirts of Colombo, Xinhua reported.
The headquarters was the venue for a human rights exhibition on the many who have disappeared during the country's protracted conflict.
Dozens of supporters belonging to the extremist Buddhist Power Force blockaded the building and then stormed it alleging the UNP was harbouring "extremist elements" inside.
Police brought the situation under control after several hours. Police later arrested one person attending the exhibition on suspicion of having ties with the vanquished Tamil Tigers.
"Due to repressive acts by the government, the UNP has decided that we will not attend the opening ceremony nor will we attend the sessions over the weekend," Tissa Attanayake of UNP said.
UNP leader Ranil Wickremesinghe was expected to attend the CHOGM opening ceremony presided over by Prince Charles and President Rajapaksa.
Pakistan Prime Minister Sharif congratulated Sri Lanka for hosting the summit. He also praised the "astute leadership" of Rajapaksa, saying the Commonwealth would become stronger and more cohesive under him.
Meanwhile, Sri Lanka was set to sign investment deals worth $2 billion on the sidelines of the summit.
Investment Promotion Minister Lakshman Yapa Abeywardana told reporters that the deals would be signed with an Australian company and two Chinese companies, Xinhua reported.