Capaldi, who was in New Zealand for a fan event last week, is then chased through Jackson's house by a Dalek.
Not only does Jackson sign the contract in the video, the Lord of the Rings and Hobbit director says he'd rather do it over six months in New Zealand rather than 12 days in Cardiff.
He also says Doctor Who showrunner Steven Moffat is constantly emailing him, but he only replies when he can understand them.
Rumours of Jackson directing a Doctor Who episode first started three years ago when he was asked the Doctor Who at the time, Matt Smith.
When interviewed by the Herald last week, Capaldi said, "I think that would be great," when asked about Jackson's possible involvement.
"Anyone who is involved in our show, it is important that they are sincere about it. Apart from the fact he is such a fabulous director I know for a fact he really cares about it and they are the most important components to have when you are making a show like Doctor Who.
"Because sometimes we don't have as much money as it appears and it can be quite tight so you need that extra bit of love to get the results."
Fans also pointed to another aspect of the video that might mean something - a copy of JRR Tolkein's The Silmarillion on the table, which Jackson is also rumoured to be adapting.
- nzherald.co.nz