The warrant, one of the most dramatic documents in British history, will go on display at the Lambeth Palace Library.
Mary, a Catholic who claimed the crowns of both Scotland and England, was executed in February 1587 in Northamptonshire. Elizabeth I is said to have reluctantly signed the death warrant at the behest of her privy council.
"She (Elizabeth) was prevaricating. To execute a monarch was such a dramatic thing in international politics," said Lambeth librarian and archivist Richard Palmer.
The library paid 72,485 pounds to a Californian auction house for the warrant, with the money raised from heritage organisations and benefactors.
The manuscript instructed Henry Grey, the sixth Earl of Kent and one of two commissioners tasked with the execution, to "repair to our Castle of Fotheringhaye where the said queene of Scottes is in custodie and cause by your commaundement execution to be don uppon her person."
In November, Culture Minister Margaret Hodge placed a temporary ban on exporting the document, on advice from the British Library that it was "so closely connected with our history and national life that its departure would be a misfortune."
The original warrant was lost in the immediate aftermath of Mary's execution. This contemporaneous copy, complete with the annotations of then principal clerk to the Council Robert Beale, now joins the covering letter sent to Grey by the Council.
"The library is delighted to have played its part in saving this document for the nation," Palmer said. "The warrant is now reunited with the papers with which it belongs and accessible for the benefit of all."
The library is in talks with various Scottish institutions about a future tour of the collection relating to a potent symbol of Scotland's history.