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.
Back on a dais, the Queen chatted to Letizia as they watched the men walk along the line of guardsmen.
Both royal couples looked the picture of elegance as they greeted each other on Horse Guards Parade, and the lavish event appeared to go off without a hitch.
The EU annoyed Britain and Gibraltar in April by suggesting Spain has a right of veto over the territory's post-Brexit relationship with the bloc. Felipe rode with the queen in the 1902 State Landau, a gilded carriage built for the coronation of King Edward VII, while Philip travelled with Letizia in a separate carriage.More news: Mithali Raj becomes highest run scorer in ODI
They will then visit Exeter college, where a professorship in Spanish is named after Felipe's great-grandfather, Alfonso XIII, and meet Spanish students and academics.
With a population of around 30,000, Gibraltar was ceded to Britain by Spain under the treaty of Utrecht in 1713.
Britain is annoyed with Spain and the European Union because Brussels has said Spain should have veto rights on any agreements regarding Gibraltar during Brexit talks.More news: Marks & Spencer share price: United Kingdom sales dip in Q1
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.
King Felipe, 49, is thought to raise the issue of Gibraltar during his visit this week and will deliver an address at Westminmster from the Royal Gallery to parliamentarians today before meeting Theresa May for talks at Downing Street tomorrow.
The Duchess of Cambridge accessorized the gown's neckline with a ruby encrusted diamond necklace owned by Queen Elizabeth II. The last such visit from Spain was made by King Juan Carlos I and Queen Sofia in 1986.More news: Viewings for Fallen NYPD Officer to Be Held Monday in the Bronx