Agyeman will replace Billie Piper, whose character Rose Tyler makes a dramatic exit from the show this Saturday after nearly two series.
Although the programme already has a prominent black character in Tyler's boyfriend Mickey Smith, played by Noel Clarke, Agyeman will be the first ethnic minority actor to play the Doctor's main companion.
The 27-year-old Londoner follows in a long line of women, men and even a robotic dog, K9, who have accompanied the Doctor on his travels in his various incarnations.
A drama graduate who attended the Anna Scher Theatre School in her summer holidays, Agyeman was discovered when she auditioned for the part of Adeola, who suffered a horrific death at the hands of the Cybermen in last week's episode.
Toyin Agbetu, spokesman for the African-British media campaign group Ligali, said: "As someone who grew up watching Doctor Who, it's about time and it's a positive thing, but it's important the character is not caricatured.
"It's not just about picking someone because of their ethnicity. It's about portraying them in a way that's not one-dimensional as a lot of the Doctor's companions have been. It's important that she doesn't become a tokenistic sidekick designed to fill an ethnic minority quota, that the character is substantive and not portrayed as ethnic totty."
The BBC was criticised for its forthcoming school-based drama Shoot The Messenger, which Mr Agbetu described as "the most racist programme in its history".
Russell T Davies, the executive producer and chief scriptwriter of Doctor Who, said: "The search for a new companion had been under way for some time when I first saw Freema Agyeman. She had come in to audition for the part of Adeola in series two. Watching her during filming confirmed what an exciting new talent she was, so we called her back in to audition with David [Tennant, who plays the Doctor]. It was an immediate and sensational combination, and her range, presence and charm blew us all away."
Mr Davies said Agyeman and Tennant, who replaced Christopher Eccleston after one series to play the Doctor, were "terrific together". "The first scripts have been written, and Martha's a brilliant addition to the Tardis crew, the perfect foil for the Doctor." He said Agyeman would join the show for its third series next year.
When she won the part, the BBC swore Agyeman to silence until Piper's departure had been made official. "I've been keeping this secret from my friends for months - it's been driving me mad," said Agyeman, whose previous television work includes appearances in The Bill, Casualty, Silent Witness and Crossroads.
"Auditioning with David in secret down in Cardiff was unbelievable, but I never in my wildest dreams thought I'd actually become the new companion. Billie rightfully built up an amazing fan base and she will be missed, but I hope the fans are willing to go on new adventures with me."
Tennant said: "Freema was a joy to work with. She is not only very talented and very beautiful, she's great fun and I'm delighted she's coming on board the Tardis full time."
Travelling with the Time Lord
Susan Foreman (Carole Anne Ford)
The Doctor's 15-year-old granddaughter, Susan, joined him in the first series, but after several adventures was left on Earth.
Vicki and Steven Taylor (Maureen O'Brien and Peter Purves)
Discovered on the planet Dido in the 25th century, Vicki joined the Tardis in 1964. Taylor joined them after being rescued from the evil robot Mechanoids.
Sarah Jane Smith (Elisabeth Sladen)
Journalist Sarah Jane joined the third Doctor, Jon Pertwee in 1973, when she stowed away in the Tardis and found herself in medieval England.
Leela (Louise Jameson)
A member of the warrior Sevateem tribe, exiled for heresy, Leela forced her way on to the Tardis, to join Tom Baker's Doctor, who resembled the tribe's god, Xoanon.
K9
The robotic dog, voiced by John Leeson and David Brierly, was capable of independent thought and fitted with a handy blaster. The Doctor presented K9 and later models as gifts to three of his female companions.
Tegan Jovanka (Janet Fielding)
An Australian air hostess, Tegan entered the Tardis thinking it was a genuine police box. She witnessed Tom Baker's Doctor regenerate into Peter Davison, but left after witnessing too much death.
Mel Bush (Bonnie Langford)
A keep-fit fanatic, Mel accompanied Colin Baker and Sylvester McCoy and tried, unsuccessfully, to persuade the Doctor to take up exercise and carrot juice.
Rose Tyler (Billie Piper)
Feisty Londoner Rose Tyler was the Doctor's sidekick when the BBC revived the series in 2005, starring with Christopher Eccleston and David Tennant.
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