The Queen has paid tribute to the "common values" shared between Indonesia and Britain at a state banquet for the Indonesian president.
Susilo Bambang Yudhoyono, 59, became the first world leader to make a state visit to the UK in the Queen's Diamond Jubilee year.
Her Majesty said Indonesia has "performed a remarkable transformation" under his leadership.
Mr Yudhoyono and his wife are spending three days in the UK.
The Queen said: "We share a common interest in a successful global economy underpinned by free trade.
"The United Kingdom is the second-largest European investor in Indonesia and we have a strong presence in areas such as financial services, energy and the creative industries.
"A spirit of togetherness and co-operation has been the hallmark of this year and, in this spirit, I am confident that if we work together on our shared aspiration to build a prosperous world based on fundamental freedoms, the partnership between the United Kingdom and Indonesia will continue to flourish."
She also said the country was now "a thriving democracy and one of the world's fastest growing economies which is playing a greater role on the international stage".
Delivering his own speech in Indonesian, Mr Yudhoyono described the Queen as an "inspiration for perseverance, dedication and loyalty".
He added: "I wish to express my sincerest gratitude and appreciation to Your Majesty for inviting me to this beautiful and historic country."
There are usually one or two state visits per year, with the next one seeing the Amir of Kuwait arrive in the country on 27 November.
Earlier on Wednesday, Mr Yudhoyono attended a private lunch at Buckingham Palace, where he and his wife Ani Bambang Yudhoyono are staying during their visit.
The couple visited Westminster Abbey, where the president laid a wreath at the Grave of the Unknown Warrior, and went to see the Prince of Wales and the Duchess of Cornwall at Clarence House.
The president also met Prime Minister David Cameron, and later Labour leader Ed Miliband and Deputy Prime Minister Nick Clegg visited the palace to see him.
The president will meet International Development Secretary Justine Greening before ending his visit on Friday with a speech at the Indonesia-UK Business Forum.
BBC Indonesia correspondent Karishma Vaswani says Indonesians are seeing this as a very important visit.
Mr Yudhoyono is expected to receive a medal of honour from the Queen, as a recognition of the closer ties between the two countries.
The UK is the second largest investor in Indonesia and is keen to do more business there. When Mr Cameron visited Indonesia earlier this year, he said it was time to sell more British defence equipment to an important democracy.
But human rights groups say the UK is moving too quickly and that Indonesia has ignored the plight of its religious minorities, our correspondent added.
During the first day of Mr Yudhoyono's visit, human rights activist Peter Tatchell was arrested for a breach of the peace after he tried to reach the car of the Indonesian president as he left Westminster Abbey.
Mr Tatchell, who was released without charge, claimed he had wanted to peform a citizen's arrest because the president "stands accused of crimes against humanity in East Timor and West Papua", but said he was arrested when he unfurled a West Papuan flag.
Although this is the first full state visit by a foreign leader to the UK this year, the Queen did host monarchs from 26 countries for a Diamond Jubilee lunch at Windsor Castle in June.
She also hosted a lunch for Commonwealth leaders at Marlborough House on Pall Mall. She was joined by more than 70 guests including representatives of all 54 Commonwealth countries.