Felipe and Letizia will then be the Queen's quests at a State Banquet at Buckingham Palace.
The four are all descended from Queen Victoria and shared a few words before the welcome ceremony began.
Addressing members of both houses of parliament during the first Spanish state visit to Britain in 31 years, Felipe said both countries had overcome "estrangements, rivalries and disputes" in the past.
Spain earlier this year agreed to the EU's ruling on Brexit negotiations that "no agreement between the European Union and the United Kingdom can be applied to the territory of Gibraltar without an agreement between the Kingdom of Spain and the United Kingdom".
There was no sign of discord as the Spanish royals arrived at Buckingham Palace, though, with Britain treating them to the full pomp and pageantry traditionally rolled out for visiting heads of state.
United Kingdom court hearing begins for terminally ill baby
There are 18 children currently on this treatment - one of them wasn't able to do anything and now she's riding a bike, she said . A few days earlier, Pope Francis and US President Donald Trump had spoken on Twitter in favor of keeping Charlie Gard alive.
Taiwan gaffe spurs apology from the US
At a White House briefing in February, Spicer twice mispronounced Australian Prime Minister Malcolm Turnbull's name as "Trunbull". Communist China, led by Xi, is called the People's Republic of China .
Nearly 8000 California Residents were Evacuated From Fire
Island fire: Lightning also caused this fire, which is burning west of Edna in the Marble Mountain Wilderness. The fire has ravaged about 23 900 hectares and was controlled to 15 %, have informed the authorities.
The subject is likely to come up when Felipe, who used a speech to the United Nations a year ago to invite Britain "to end the colonial anachronism of Gibraltar", holds a bilateral meeting with Prime Minister Theresa May on Thursday.
Spain has a long-standing territorial claim on Gibraltar, which has been held by the United Kingdom since 1713, but Mrs May has previously insisted that Gibraltar's status will not be up for discussion during exit talks from the EU.
The Duke of Edinburgh, who recently spent a short spell in hospital, is due to accompany Felipe as he inspects the Guard of Honour, the 1st Battalion Irish Guards, on the Horse Guards Parade ground.
The VIP visitors enjoy a military ceremonial welcome on Horse Guards Parade to mark the start of their visit to Britain.
King Felipe VI, 49, is the only son of Juan Carlos and his wife Sofia of Greece and Denmark.