It was all revealed in Chapter 347 of manga series wherein Tsunade and Jiraiya reminisce the good old days while contemplating for the future of Konoha.
They confirmed all speculations that Uzumaki Naruto is indeed the son of the Fourth Hokage,Konoha’s Yello Flash; Minato Namikaze.
According to those who knew him, Minato was a very talented ninja-having graduated from the Academy at the age of ten. He came under the tutelage of Jiraiya, and under his guidance, learned to develop his skills. Impressed with Minato’s determination to succeed, Jiraiya took it upon himself to teach the latter the Toad Summoning Technique. Minato mastered the technique, being the only person to fully control Gamabunta, a feat not even his sensei could do. His skills would further grow with the development of his own jutsu, the Rasengan and Flying Thunder God Technique.
After attaining the rank of Jonin, Minato was given direction of his own team, which consisted of Kakashi Hatake, Rin and Obito Uchiha. Along with Kakashi, Minato’s reputation greatly increased during the Third Great Ninja War, where his skills earned him the moniker of Konoha’s Yellow Flash. As a gift for Kakashi’s advancement to Jonin, Minato gave him a unique kunai marked with one of the Flying Thunder God transportation markers. Shortly afterwards, he informed the team of their mission: destroy a bridge that aided the enemy Rock ninja force. For the mission, Kakashi took Minato’s place as commander of the team while he went to a different battlefield, where he was able to defeat a large number of Iwa ninja singlehandedly. His team, however, was unable to complete their mission, as differences between Obito and Kakashi lead the team to be caught in a trap. Obito, however, was unable to survive the mission, instead helping Kakashi save Rin by giving Kakashi his Sharingan eye before being completely crushed by rocks. When Rin used Kakashi’s kunai, Minato arrived and easily defeated the Iwagakure ninja. Unfortunately, by the time he arrived Obito was already dead, though he managed to save Kakashi and Rin. They would later go on to fulfill their mission and help repel the invasion.
Now for Naruto’s mother, Uzumaki Kushina,
She was the mother of Naruto Uzumaki. When she was young she was a talkative tom boy. It’s noted that she had long, red hair that came down to her lower back as seen in chapter 382. When she grew up her beauty, personality and Ninjutsu became known to many. It was this very personality and Ninjutsu skill which she would pass on to Naruto. At some point in time she met Minato Namikaze, the Fourth Hokage, and bore his child. When Jiraiya visited the couple during the pregnancy, he allowed Minato to read one of his latest books, a semi-biographical account of Jiraiya’s own life. The character in the story was known for his drive and determination. For that reason Minato asked Jiraiya if he would mind if he named his own son “Naruto” after the character in the story. Kushina offered her approval of the name choice. Jiraiya was embarrassed and honored. After the Nine-Tailed Demon Fox attacked Konoha, which resulted in the death of Minato, and the demon fox being sealed within Naruto, Kushina’s status became unknown, but she is presumed deceased as she is referred to in the past tense.