Chaitramasi jagadbrahma sasarju prathamehaani
Shukla paksha samagranthu thadaa suryodaye sathi
Pravarthayaamaasa thatha kaalasya gananaamapi
Grahantaaraan ruthoonmaasaan wathsaraanwathsaraadhipaan
Lord Brahma created the Universe on the first day of Shukla Paksha of the Chaitra month. He created the planets, stars, seasons, years and Lords of years.
From their original union during the moment of Creation; the Sun and planets have moved endlessly forward from the same spot in the sky, each at their own speed. This region is the constellation of Aries, or mesha. This is the first constellation that the Sun enters after it crosses north of the Equator, the Spring Equinox. Chaitra marks the first month after the Sun enters the constellation of mesha. The lunar cycle has the same beginning, called Meshadi or the "start of Aries". Similiarly, the grahas (planets) started from mesha as well. Let's consider the slowest members of the planets, Jupiter & Saturn. Jupiter (Brihaspati) has a daily motion of 5 kalas (angular minutes), and takes ~ 12 years to return back in mesha. Saturn (Shani) has a daily motion of 2 kalas, and takes ~ 30 years to return. This way, it takes ~60 years for both Brihaspati & Shani to come together in mesha, which marks the first year of the samvatsara cycle.
The starting date was determined by Aryabhata, who backcalculated the positions of the planets to coincide at mesha at the beginning of Kali yuga, to 3102 BCE.
The choice of 3102 BCE had a special significance for Aryabhata. Midday at Ujjain on the equinoctial day 21 March CE 499 exactly corresponds to the beginning of the year 3600 of his Kaliyuga. Since the ardharatrikapaksa (midnight school) starts its Kaliyuga six hours before the Aryapaksa, Aryabhata artificially made the duration of the year slightly longer in the former case so that in both the schools the 3600th year starts at the same time. Significantly, CE 499 is the year of the composition of Aryabhatiya.
However, it is now known that planetary orbits are subject to various kinds of perturbations, and a theory depending on the orbital period as the sole parameter cannot give accurate results. According to modern numerical simulations, on 17/18 February 3102 BC the five geocentric planets were not aligned but spread over two neighboring zodiacal signs. This again underlines the inference that the significance of the date was hypothetical rather than real. In addition, the adhikmasa (leap month) methodology as introduced by Bhaskara II worked to shift the years from their original cycle.
In the Siddhanta Jyotisha, the Samvatsaras have been counted as 60 beginning from Vijaya and going down to Nandana. But Varahamihira in Brihat Samhita regarded the beginning of the Samvatsara cycle, not from Vijaya, but from the 35th Samvatsara of Prabhava. Since Varahamihira’s times it is this sequence which has been accepted.
For an astrological explanation, see here.