At the start of the two-day visit, the leaders of the African nation with the biggest population - triple that of the UK - were greeted by senior royals including Queen Camilla, and the Prince and Princess of Wales.
The King and President Tinubu will give speeches on Wednesday evening at the state banquet, which will be attended by political leaders and celebrities with links to Nigeria.
However, there will be no traditional lunch with the King at Windsor as the president is a Muslim and fasting for Ramadan.
The president and first lady, who arrived in the UK on Tuesday, were given the ceremonial grandeur of a royal welcome, with a carriage procession and then a military parade on the manicured lawns inside Windsor Castle.
They were met by Prince William and Catherine, Princess of Wales, at the luxury spa hotel Fairmont Windsor Park before being escorted to the town to formally meet the King and Queen.
As the carriage procession carrying the King and president arrived into Windsor Castle's quadrangle they were met by a guard of honour and the band of the Grenadier Guards - which played the Nigerian and British national anthems as they travelled round the square.
In the spring sunshine, Tinubu then ceremonially inspected the troops on display, with King Charles walking a few steps behind.
State visits are a way of building relationships with international partners and the Nigeria visit will see a strengthening of business links, including financial services.
More than 270,000 Nigerian-born people live in the UK.
"This state visit is about turning a historic relationship into a modern economic partnership - transforming trust into opportunity," said Nigeria's government spokesman, Mohammed Idris.
"Nigeria's economic reforms are unlocking the potential of Africa's largest consumer market. The United Kingdom is a natural partner in what comes next.
"This visit marks the next step in deepening co-operation across trade, finance and defence," said Idris.
Later, there will be exchanges of gifts and displays of items related to Nigeria that are kept in the Royal Collection, before an opulent state banquet in St George's Hall.
President Tinubu and his Christian wife will lay a wreath of flowers on the tomb of the late Queen Elizabeth II, in St George's Chapel.
The couple will also attend an interfaith event, designed to build bridges between religions.
On Thursday, Mrs Tinubu, who is also an ordained pastor, is set to preach at a service at Lambeth Palace and meet representatives from the Church of England.
The Tinubus are from the Yoruba community of the south-west, one of the country's largest ethnic groups that is divided between Muslims and Christians.
In fact, Nigeria's 220 million people are roughly evenly split between followers of the two religions, with mostly Muslims in the north and largely Christians in the south.
President Tinubu faces growing international pressure to tackle insecurity and better protect vulnerable groups - in particular from the administration of US President Donald Trump, which has raised concerns about the treatment of Christians in Nigeria.
Though the Nigerian government says members of all faiths have suffered amidst the country's numerous and overlapping and security challenges, including an Islamist insurgency, kidnappings for ransom by criminal gangs, clashes over land and separatist unrest - which often play on ethnic as well as religious identity.
In the north-eastern state of Borno state this week at least 23 people were killed and 108 injured by a series of suspected suicide bombings, blamed on hard-line Islamist militants from the Boko Haram group.
President Tinubu condemned the "evil-minded" terror groups - and MPs in the UK have called for the protection of freedom of worship in Nigeria.
The visit takes place against the backdrop of war in the Middle East as well as the conflict in Ukraine - with Ukraine's President Zelensky meeting King Charles on Tuesday.
The banquet will also see the King's first speech since the arrest of his brother Andrew Mountbatten-Windsor.
