Arthur Simpson-Kent left the UK on 19 December after the deaths of Ms Blake, 43, and their two young sons, Zachary, aged eight and Amon, aged four.
Their bodies were found buried in the garden of their family home in Erith, south London, on 5 January.
Mr Simpson-Kent is due at Westminster Magistrates' Court on Friday.
Ms Blake, who played Frankie Pierre in 56 episodes of EastEnders in 1996 and 1997, died from neck and head injuries, post-mortem tests found. She had been suffering from motor neurone disease.
Her sons also died from head and neck injuries.
Four days after their bodies were found, police officers arrested Mr Simpson-Kent on a beach in Ghana.
He was remanded in custody in Ghana on 12 January and appeared in Kaneshie Magistrates' Court in Accra.
Mr Simpson-Kent was arrested after locals recognised him from a social media photo and tipped off police.
The Met was criticised over delays in its investigation after it emerged officers spoke to Mr Simpson-Kent at the family home on 16 December.
They returned two days later to find the house empty.
But it was not until early January that the bodies of Ms Blake and her sons were found in the garden.
The Met's handling of the case is being investigated by the Independent Police Complaints Commission.

Winds reached 36mph and blew trees over at Emirates Golf Club, where play has stopped until Saturday, angering some of the 64 players to finish round two.
Former Masters champion Trevor Immelman called the halt "ridiculous", while Ryder Cup player Chris Wood said the decision made the event "one sided".
Tournament director Mike Stewart said the course was "unsafe and unplayable".
Stewart added: "We had TV towers that the roofs were blown off. We had balls moving on the greens - blew into a bunker at one stage. Five trees came down."
There are 65 players, including George Coetzee of South Africa, who leads on nine under, and Spaniard Sergio Garcia, a shot behind, who have nine holes or more left to play of round two.
England's Matthew Fitzpatrick (three under par), Danny Willett (one over), Ian Poulter (three under) and Northern Ireland's Graeme McDowell (four under), are all yet to reach halfway in the second round.
Stewart still thinks the tournament will conclude on Sunday as round two will be completed on Saturday with the third round commencing later in the day from a two-tee start.
However, a host of early starters on Friday stressed their frustrations as those set to face the gusts later in the afternoon were spared.
Spain's Pablo Larrazabal - who ended five over after two rounds - said he was "very angry".
South African Immelman, who is set to miss the cut at four over par, wrote on social media: "Suspending play now is ridiculous, half the field played 36 holes in these conditions."
Martin Kaymer of Germany, who is tied for fifth on four under, said: "Hard to understand the difference between the morning play and now, therefore even more surprised about the decision."
Earlier on Friday, 14-time major winner Tiger Woods withdrew from the tournament before the start of round two citing a back spasm.
The 41-year-old American, who only returned to action in December after 15 months out following two back operations, was five over after 18 holes.
The partner of EastEnders actress Sian Blake, whose body was found in their garden, is to be flown back from Ghana to the UK later, prosecutors have said.
[NEXT_CONCEPT]
Players have criticised the European Tour's decision to suspend round two of the Dubai Desert Classic in Abu Dhabi.