In the painting, the Queen wears her garter robes as she sits in the White Drawing Room at Windsor Castle.
The artwork, which was unveiled at Windsor Castle, is by artist Henry Ward, who was born in Essex but now lives in Canada.
The Queen is the longest-serving patron of the charity, which supports people in crisis in the UK and overseas.
She has supported the British Red Cross by visiting projects and offices and attending and hosting events, such as a Buckingham Palace garden party to celebrate 100 years of the organisation.
The new portrait contains imagery which highlights the long-standing relationship between the Royal Family and the Red Cross, whose first royal patron was Queen Victoria.
It includes a bust of Henry Dunant, who founded the organisation, and the Queen is wearing diamond earrings, a bracelet and a tiara which belonged to Queen Alexandra.
She signed the petition for the granting of the British Red Cross Royal Charter before it was presented to her husband, King Edward VII.
Artist Mr Ward was chosen by the Red Cross because of his support of the charity.
He said: "As a long-standing supporter of the British Red Cross, it has been an honour to paint the Queen to celebrate six decades of her patronage.
"To portray Her Majesty as monarch and as patron of the Red Cross I have included imagery that relates to the history of the relationship.
"I have also been influenced by previous royal portraitists such as Anthony van Dyck and Sir Joshua Reynolds."
A new portrait to mark the Queen's six decades as patron of the British Red Cross has been unveiled by the monarch.