Both songs will appear on the British band's upcoming new double album, "Everyday Life," which is due on November 22.
"Champion of the World" arrived with a stylized lyric video, while "Daddy" came along with an accompanying animated video from Aardman Studios and directed by Bristol-based filmmaker Åsa Lucander.
In a statement announcing both songs, Coldplay detailed the inspiration behind the animated clip for "Daddy," which "offers an atmospheric journey through a girl's fragmented memory about her father."
"A few minutes into listening to the track 'Daddy' -- it spoke to me in a way that stories and visual images began to dance in front of me. And when this happens you know that you are on to something very special indeed. I tend to get drawn to emotional stories and this was certainly one I wanted to tell," Lucander added.
"Champion of the World" was notably co-written by the late frontman of Scottish indie band Frightened Rabbit, Scott Hutchison, who passed away at the age of 36 on May 2018.
In a statement, Coldplay vocalist Chris Martin revealed that the song is based on Hutchison's "Los Angeles, Be Kind," which appeared on his 2014 solo album released under the moniker Owl John.
"When I first heard it, I thought it was going to go one way; but it went another. Anyway 'Champion Of The World' is the song that came from following the other path, and that's why Scott is a co-writer on this song. Today is also his birthday. So happy birthday Scott and thank you for your beautiful music, wherever you are," he added.
"Daddy" and "Champion of the World" are respectively the fourth and fifth cuts from "Everyday Life" to be released, following the previously issued "Arabesque," "Orphan" and the title track.
The double album, which is composed of "Sunrise" and "Sunset," will mark Coldplay's eighth studio effort following their 2015 "A Head Full of Dreams."
The band will accompany the release of "Everyday Life" with a two-part livestream performance from Amman, Jordan, beginning with a "Sunrise" concert at 4 a.m. (GMT) and followed by a "Sunset" concert at 2 p.m. (GMT).
"These two broadcasts have been our dream since we first started work on this album. It's a bit impossible and a bit scary, like all the best dreams. YouTube is the perfect home for it," the band said in a statement.
Earlier this week, Coldplay announced that they have put plans to tour in support of their new double album on hold, due to concerns about the environmental impacts of concerts.
"We're taking time over the next year or two, to work out how our tour can not only be sustainable [but] how it can be actively beneficial," the band told BBC News, adding that they are thinking of having a show with no single-use plastic or largely solar-powered.
Although they will not be touring "Everyday Life," Coldplay will perform a one-off concert at London's Natural History Museum on November 25, with all proceeds going to an environmental charity.