The Kellog's jingle is provided in the clip here:
http://www.youtube.com/watch?v=9sfdlsExCU8
The original 1939 song "Good Morning," from Babes in Arms" and more famously later in "Singin' in the Rain," is here:
http://www.youtube.com/watch?v=aSrRFKlL7As
Personally, I only find a slight similarity between the melodies, and "good morning, good morning" the only similar lyrics. Nevertheless, some people believe there is a connection: 'J LeeOctober 3, 2010 6:41 AM
Hanna-Barbera did have to do a little reanimation on the titles for the 1959-60 season, due to both the growing popularity of Yogi Bear (Yogi gets a walk-on with Huck to start the Season 2 end titles) and the fact that Kellogg's modified their slogan in early 1959 adding "The Best To You Each Morning," tag that was based off the 1930s song "Good Morning".' -from
http://yowpyowp.blogspot.com/2010/10/wrong-ipedia.html
Officially, there does not seem to be any acknowledgement that the jingle was based on the song:
'In the 1950s, Kellogg's introduced its first sweetened cereals... ...Later in the decade, Kellogg's introduced a new slogan: "The Best to You Each Morning."' -from
http://www.encyclopedia.com/topic/Kellogg_Company.aspx#4
'During the decade of the 1950s, the years of "I like Ike" and Pax Americana, the Leo Burnett Company was able to reflect the American values of strength, tradition, comfort, and family in its advertising campaigns. This talent won for the agency a number of new and profitable clients and secured those accounts already in the Burnett agency... ...Similarly, the thematic catch phrases of "the best to you each morning" for Kellogg's and "you're in good hands" for Allstate carry with them a familial warmth and all-American appeal.' -from
http://www.fundinguniverse.com/company-histories/leo-burnett-company-inc-history/
Incidentally, 'John Lennon wrote the song "Good Morning Good Morning" after seeing a Kellogg's® Corn Flakes commercial on TV. The black and white commercial simply featured Kellogg's® Corn Flakes being tipped into a bowl. The song's chorus and title came from the jingle "Good morning good morning...the best to you each morning... sunshine breakfast...Kellogg's® Corn Flakes crisp and fun".' -from
https://www.lyrics.com/lyric/32537843/The+Beatles/Good+Morning+Good+Morning