Both actors have portrayed Prince Philip in the hit Netflix drama, which is based on the lives of the royal family.
He said: “I’d like to offer my condolences to Her Majesty the Queen and the Royal Family.
“Prince Philip was the man. And he knew it. 99 and out, but what an innings. And what style.
“Thank you for your service old chap – it won’t be the same without you.”
Matt was replaced in The Crown by Tobias for series three and four, opposite Olivia Colman as the Queen.
Tobias wrote on Twitter: “If I know anything about the Duke of Edinburgh I’m fairly sure he wouldn’t want an actor who portrayed him on TV giving their opinion on his life, so I’ll leave it to Shakespeare.
“‘O good old man! how well in thee appears. The constant service of the antique world…’ RIP.”
A statement from the show, written by Peter Morgan, said: “Netflix, Left Bank Pictures, Sony Pictures Television and the production team on The Crown are deeply saddened to hear of the death of The Duke of Edinburgh.
“Our thoughts are with the royal family at this sad time.”
Oscar nominee Jonathan Pryce will take over the role of the Duke of Edinburgh for the fifth and six series of the show, which will be the last.
He will star opposite Imelda Staunton as the Queen.
The Duke of Edinburgh passed away at Windsor Castle on Friday morning.
Last month, he was discharged from hospital after a month-long stay to treat a heart condition.
Following the news of his death, a number of other names from the entertainment world also paid tribute to him online.