They are being funded from the $604 million Budget boost for the government's drug-buying agency Pharmac, announced in June.
Associate Health Minister with responsibility for Pharmac David Seymour said from Sunday, an estimated 112 patients would be able to access Lenvatinib (branded as Lenvima) for thyroid, liver and kidney cancer.
Pharmac chief medical officer Dr David Hughes said the medicine stopped cancer cells from multiplying, slowing the disease's progression.
He said previously, patients with specific types and stages of thyroid and liver cancer had only received "supportive care that provides comfort and relief from their symptoms".
Seymour said also funded from today were β-hCG low sensitivity urine test kits, which meant an estimated 9300 women would be able to test whether their abortion was effective at home, rather than having to get a blood test.
The testing kit (branded as CheckToP) detects the levels of hormones in the body through a urine sample.
Pharmac spokesperson Alexandra Compton said the agency's public consultation on CheckToP found it would make managing an abortion easier, especially for people in rural areas.
People with ADHD who meet certain eligibility criteria would also be able to access funded Lisdexamfetamine from Sunday. This was expected to benefit more than 6000 people in the first year.
"This will provide an additional once daily treatment option for the management of ADHD while also easing the pressure on the supply of other ADHD medicines," Seymour said.
And thousands of New Zealanders suffering from chronic heart failure now have access to Empagliflozin - a daily tablet that helps the heart pump blood around the body, reducing swelling and making it easier to breathe.
Pharmac first funded the medicine in 2020 for some people with type 2 diabetes, but from this month it will widen access to people with a certain type of long-term heart failure.
"The $604 million will also enable an estimated 18,000 patients with chronic heart failure with reduced ejection fraction. Pharmac anticipates this number to grow, after five years an estimated 33,000 additional people would benefit from empagliflozin every year," Seymour said.