The aircraft, made under license from BAE Systems' aerospace division, was delivered during a ceremony at HAL's Bangalore plant, a statement by HAL said.
"We built this aircraft on time, the first of the five aircraft to be delivered to the Indian navy. The remaining four will be delivered soon," HAL Chairman R.K. Tyagi said.
"We are carrying forward this legacy and will ensure that [the] navy gets all the support from HAL on all parameters," he added.
Vice Adm. Pradeep K. Chatterjee said the navy has had a longstanding partnership with HAL and "will continue to work shoulder to shoulder for all our current and future programs."
HAL said the five trainer jets to be delivered by the end of the fiscal year are part of a larger order from the navy for 17 aircraft to be delivered by 2016.
The Ministry of Defense ordered the navy's Hawks, as well as 40 more Hawks for the air force, in 2010. Their primary use is for training pilots, but the Hawk can be upgraded quickly to be used as a ground attack aircraft, HAL said.
India is now the third naval operator of Hawk trainers, along with the U.S. Navy and that of the United Kingdom, a statement from BAE Systems said.
Among its 18 customers worldwide, India is the largest operator. India's air force already has 70 of the two-seat trainers, which are powered by a single Rolls Royce Adour Mk 871 engine.
Guy Griffiths, BAE Systems Group' managing international director, said the handover to the navy "marks another significant milestone" for BAE and HAL.
"We also have submitted our response to HAL's request for proposal to supply products and services for the manufacture of 20 additional Hawk aircraft to the air force and now are looking forward to partnering with HAL in providing the Indian air force's display team."
The air force's national Surya Kiran Aerobatics Team will fly Hawks, although the switch to the new planes may not be occur until 2016 because of priority manufacturing for the navy and air force.
SKAT announced the switch in October 2011, saying the Hawks will replace the Kiran Mark II trainers that the team has been flying since 1996.
The Indian-made and designed Kiran, originally powered by a Rolls-Royce Viper Mk II engine, was flown for the first time in 1964.
The Kiran Mark II, a more powerful Hawk version, is powered by a Bristol Siddeley Orpheus engine and has improved weapon-carrying capability. It first flew in 1976 and entered service in 1985. Production ended in 1989 after 61 were built.