The £1m painting was made by Francis Hayman just after the 1740 publication of Richardson's most famous work, his debut novel Pamela or Virtue Rewarded.
It shows the writer with a book in his hand accompanied by members of his second family.
The Tate was able to buy the painting with a grant from the Art Fund.
The painting - entitled Samuel Richardson, The Novelist (1689-1761), Seated Surrounded By His Second Family - is considered one of the most important "conversation piece" paintings, a type of informal portrait in which sitters would appear in domestic or private settings.
"This portrait captures a fascinating moment in the novelist's life just after he had become an overnight sensation," said David Barrie, director of the Art Fund, which gave a total of £150,000 towards the purchase of the picture.
"The portrait is undoubtedly one of Hayman's best, and after decades in a private collection The Art Fund is delighted that it can at last be appreciated by the public."
Richardson's novel Pamela or Virtue Rewarded tells the story of a young maid who refuses the advances of a richer householder until he agrees to marry her.
It was so loved by the mid-18th century middle-classes that it went through five print runs within a year of publication. It also influenced some of the biggest names in literature, such as Jane Austen and Jean-Jacques Rousseau.
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