The queen received Yudhoyono and his wife Ani with a guard of honour on Horse Guards Parade, the large parade ground in central London, where the visiting leader inspected the troops in their scarlet uniforms and bearskin hats.
The 86-year-old British monarch and her husband Prince Philip then accompanied them in a horsedrawn state carriage procession along the Mall to Buckingham Palace, where the visiting couple are staying during their trip.
The queen, who visited Indonesia 33 years ago with Philip, will host a lavish state banquet in Yudhoyono's honour on Wednesday evening.
Foreign Secretary William Hague and Home Secretary Theresa May also greeted Yudhoyono and his wife before the carriage procession.
"As well having one of the world's most thriving economies, Indonesia is in the vanguard of the political change shaping Asia," Hague told parliament on Tuesday.
"This visit will be an opportunity for us to build on the strong partnership established over the last decade."
The president will hold talks with British Prime Minister David Cameron on Thursday and attend a meeting of the high-level United Nations panel that is drawing up a strategy on how to build on the Millennium Development Goals.
Yudhoyono, who is the world's only head of state to have served as a UN peacekeeper, will also give a speech at the Royal College of Defence Studies.
The 15th-century Guildhall, in London's financial district, will host a second banquet on Thursday night.
Several trade announcements are expected during the three-day trip, with Britain keen to gain access to Indonesia's fast-growing economy and 240 million consumers.
The state visit is part of Britain's drive to boost its diplomatic presence in Southeast Asia, with Indonesia regarded by British officials as the most influential player in the region.
As the world's largest Muslim-majority country, it is also seen as a strategic ally in the Islamic world.
"Indonesia is far and away the most important country in ASEAN," said a Foreign Office source.
Officials also see Indonesia as a potential future host for foreign campuses of its universities, similar to Malaysia where several British universities including Nottingham, Southampton and Newcastle have outposts.
Britain usually hosts two state visits each year, but Yudhoyono is the only foreign head of state to receive the formal hospitality in 2012 following months of diamond jubilee celebrations marking the queen's 60th year on the throne.
The last state visit was by Turkish President Abdullah Gul in November last year.
Copyright AFP (Agence France-Presse), 2012