The move confirms last year's scrapping of the 1% pay cap and follows campaigns by unions for higher wage rises.
The Government said the increases were affordable within its spending plans.Ministers said members of the armed forces will receive an increase of 2.9% (2% consolidated, 0.9% non-consolidated), with Tuesday's award worth £680 in pay to an average soldier, plus a one-off payment of £300.
The teachers' award means the main pay range will increase by 3.5% (2% to upper pay range and 1.5% to leadership). Schools will determine how it is set.
All prison officers will get at least a 2.75% (2% consolidated, 0.75% non-consolidated) increase this year, with many getting higher awards.
A police award of 2% will mean average pay for a constable will now be more than £38,600 a year.
A pay increase of at least 2% will be given to junior doctors, specialist doctors, GPs and dentists. Consultants will also get a pay rise of at least £1,150.
Ministers said teachers are in line for a pay rise of up to £1,366 a year.
Education Secretary Damian Hinds said there will be an investment of £508 million to fully fund the deal.
-> Death toll rises as wildfires hit holiday resorts near AthensHe said: "There are no great schools without great teachers and I want to us to recruit and retain brilliant teachers who are fairly rewarded for the vital work they do.
"Today we are announcing a fully funded pay rise of up to 3.5% - or between £800 and £1,366 - for classroom teachers on the main pay range, 2% for those on the upper pay range and 1.5% for those in leadership positions.
"This will mean that teaching continues to be a competitively rewarded career, and I will continue to work with the profession, Ofsted and the unions on issues like excessive workload, professional development and flexible working, to make sure teaching remains an attractive, fulfilling profession."
Schools will continue to determine how their staff are paid but the increases will be funded with a new teachers' pay grant - worth £187 million in 2018/19 and £321 million in 2019/20 from the existing Department for Education budget - paid to all schools on top of their core budgets from the National Funding Formula, said the Government.
In cash terms, teachers could receive a boost of between £1,184 and £1,366 to their salary, while salaries for new teachers will increase by between £802 and £1,003.
Prospect union deputy general secretary Garry Graham said: "Today's pay deals for the armed forces, prison workers and teachers are welcome but confirm what we have long suspected - this Government have put civil servants firmly at the back of the queue on public sector pay.
"Instead of playing cynical divide-and-rule games with overworked and underpaid public sector workers, the Government should be committing to above-inflation pay rises for all public servants, with no group left behind."
-> Ministry of Defence to sell RAF base in YorkshireHealth and Social Care Secretary Matt Hancock said the pay rises for doctors and dentists recognised their "value and dedication" and took into account affordability and the prioritising of patient care.
From October, a consultant starting work in 2013 will have seen a 16.5% increase in their basic pay, rising to a salary of £87,665 from £75,249, it was announced.
Ministers said the pay rises were worth between £1,150 and £1,550 for consultants, between £1,140 and £2,120 for specialty doctors, between £1,600 and £2,630 for associate specialists, between £532 and £924 for junior doctors, and around £1,052 for a salaried GP with a median taxable income of £52,600.