The monarch, who used a golf buggy to tour the Chelsea Flower Show on Monday, met with the ruler, Sheikh Tamim bin Hamad Al Thani, on Tuesday afternoon.
The 96-year-old, whose Platinum Jubilee national celebrations are just over a week away, was pictured standing, shaking hands with the Emir in her Oak Room sitting room.
Wearing a blue and green floral dress, the Queen smiled broadly as she greeted her guest.
Earlier on Tuesday, the Emir used a bilateral discussion with Prime Minister Boris Johnson to invite him to travel to watch the winter 2022 World Cup in Qatar.
The tournament has been dogged by human rights controversies in relation to migrant worker abuses during the construction of stadiums in the country.
Qatar’s right to stage the major sporting event was publicly questioned at the Fifa Congress in Doha in March, with the president of the Norwegian federation saying there was “no room” for hosts who could not legally guarantee the safety of LGBTQI+ people.
Same-sex relationships are directly criminalised under the laws of the Gulf state, leading to concerns over the well-being of LGBTQI+ people visiting for the tournament and those from that community who reside there.
Fifa and the Supreme Committee insist supporters from the LGBTIQ+ community will be made welcome.