Kitayama finished second to Xander Schauffele at The Reniassance Club, having set the clubhouse target at six under after a superb 66 on Sunday.
Three places at St Andrews were up for grabs for players not already qualified as long as they finished in the top 10 in North Berwick.
Wu played his way in with a 67 and Welshman Donaldson, a star of the 2014 Ryder Cup, matched his score.
The pair finished in a tie for sixth with Matt Fitzpatrick and Cameron Tringale, four shots off the seven-under winning total of Schauffele.
Kitayama said: "It's really exciting. Being the 150th, there's a lot of hype around it. So I'm looking forward to that. It's going to be really cool. I've actually never played there. Missed out on the Dunhill. It's going to be really exciting."
Donaldson, who fired three birdies in four holes from the 12th to make it, said: "It’s my first appearance in The Open since 2016 so it’s fantastic to be able to play St Andrews again, something I’ve done before. For the 150th Open it’s extra special to be there.
“I played really good today and the three birdies on the back nine were really big for me. To have five birdies and only two dropped shots, it was a good day’s golf as it was difficult out there if you were out of position.
“It’s difficult knowing you have to post a score to reach The Open. I’ve been here before when I nearly got into Royal Portrush in 2019 so it’s nice to do it this time around.”
Wu said: “It’s honestly so incredible to be playing in The 150th Open at St Andrews. It’s so remarkable for me. I played well today but I just needed a little bit of help from others at the end.
“It’s a tough closing stretch and the 18th played so difficult today. I waited to see Rasmus (Højgaard) finish but then just couldn’t watch and thought 'whatever happens will happen'.
“It’s good to have the experience of playing in The Open before at Royal Portrush which was a really difficult course. Three years later it will be good to measure myself again against players at the very highest level.”