Modi, who in his departure statement said the fact that he was visiting Nepal twice in the six months since he took over "reflects the importance we attach to our unique and special relations with Nepal", also held delegation-level talks with his Nepali counterpart Sushil Koirala.
Modi, who is here to attend the 18th SAARC Summit, urged Nepal to frame its much-awaited constitution early and on the basis of consensus.
Addressing a gathering during handing over of a 200-bed trauma centre built by India, Modi said writing the constitution was "taking too much time" and urged Nepal to finish the work on the basis of consensus and not majority.
He said the constitution should be like a bouquet, with each flower representing each strata of the Nepali society - the Madhesis, the Maoists and Pahadis - providing them rights.
Modi said India will not interfere and has never interfered in Nepal's affairs, but added that "Nepal's happiness is reason for us to smile, so write it fast".
Political parties have set Jan 22 as the deadline to draft the constitution.
The trauma centre has been built by India at a cost of Rs.1.5 billion in the city's Bir Hospital, the oldest medical facility in the country.
Among the dozen agreements inked was one for project development agreement (PDA) for the Arun III Hydropower project.
Both sides also kicked off a Kathmandu-Delhi bus service being run by the Delhi Transport Corporation (DTC).
Modi also handed over the keys of a Dhruv Advanced Light Helicopter to the Nepali army and a mobile soil testing laboratory to the country.
He said a "lot of trust" has been put into their bilateral relations.
A "big horsepower engine" of trust has been fitted into their relations in the 100 days since his last visit to Nepal in August, he said.
Referring to his decision not to visit Lumbini, the birthplace of Lord Buddha, as well as Janakpur and Muktinath, which both Hindus and Buddhists hold as sacred, Modi said it was due to paucity of time.
"This time, I was keen to go by road because I wanted to see the difficulties the people of Nepal and Indians on that side face and help mend matters. But due to shortage of time, I could not do it," he said.
The prime minister said he was aware of the disappointment of the people in the three places and assured them that he will visit them in the near future.
He said the bilateral decisions that were stuck for the past 25 years were now being pushed forward.
"Between my first visit, and my second, decisions have been taken to change lives in Nepal, and give happiness to India," the prime minister said.
Modi said the hydropower projects - Pancheshwor, Upper Karnali and Arun III - that were stuck for many years have been pushed forward and that all the Nepal parties have shown farsightedness in backing the projects with India.
He said a new electricity transmission line was being set up between the two countries.
"One new transmission line of 1,000 MW is being installed, and Nepal will light up," he said.
Modi said the $1 billion line of credit which he had announced during his last visit was being finalised.
Both countries also inked the Motor Vehicles Act that would allow regular bus service between the two nations.
The other agreements and memoranda of understanding (MoUs) inked include on setting up of a Nepal Police Academy, on tourism and traditional medicines, Sister City Agreements between Janakpur and Ayodhya, Kathmandu and Vanarasi, and Lumbini and Bodhgaya.
Modi later called on President Ram Baran Yadav at his office in Sheetal Niwas.
The Indian prime minister also held a meeting with leaders of the largest party Nepali Congress at Soaltee Hotel, where he is staying, as well as with members of other political parties.