Was it Minato who invented the Rasengan, or was it Jiraya? All I know is that Jiraiya taught Naruto the Rasengan. Who is the original creator?
The Rasengan is an A-rank technique created by the Fourth Hokage, Minato Namikaze, by observing the Tailed Beast Ball. Minato spent three years developing the Rasengan.
Jiraiya taught Naruto how to create and use Rasengan.
It was Minato. The Fourth Hokage invented in from seeing the Bijuu-dama. Jiraiya learned it from Minato and then taught Naruto about it. See Rasengan article on Naruto Wiki.
Edit: While it wasn't mentioned which Bijuu Minato based his Rasengan from, it is presumably the Kyuubi as the Kyuubi was the only Bijuu in possession of Konoha at that time and the Jinchuuriki is his wife.
No, it wasn't Minato or Jiraiya who invented Rasengan. If you watch Naruto from the beginning to the last (Naruto Shippuden), Rasengan was made by Ashura, one of Hagoromo's sons. It means Rasengan has been invented a long time ago, even before Minato was born.
The true inventer is Ashura. Yes, Minato worked so hard to make it but he was sadly not the person who invented it. Around episodes 400-500 there is an episode where Ashura and Indra fight; Indra has the full Susanoo and Ashura has the Truth Seeker Orbs. After about 7 minutes, Ashura makes a Rasangan with like 4-5 mini Rasangans in it. So the part that Minato "invented" it is false, he just happens to have revived a really old ninjutsu. So in his way he "invented" it.
It is true Ashura made the first Rasengan, but as far as who did it first between Jiraiya or Minato, Jiraiya did tell Naruto that the 4th Hokage invented it.
There's an episode, I believe 33 of season 1 Shippuden, showing that Jiraiya mastered that jutsu in way less time.