Members of the Rail, Maritime and Transport (RMT) union will walk out for 24 hours from 5pm on June 4 and for 48 hours from the same time on June 9.
The workers, including signallers and maintenance staff, will also ban overtime from June 6-12.
A planned strike over the bank holiday was suspended after Network Rail tabled a fresh pay offer.
But a meeting of RMT reps rejected the improved deal, leading to fresh strikes being announced.
The industrial action is expected to cause widespread disruption to rail travel, sparking travel chaos across the country.
NR had originally offered a four-year deal - £500 this year followed by three years of increases in line with RPI inflation.
The new offer was for two years - a 1% rise this year and around 1.4% next year, with no compulsory redundancies for the duration of the agreement.
RMT general secretary Mick Cash said: “Our representatives have today rejected the pay package offered by Network Rail and, in the absence of any further movement from the company, that has left us with no option but to move to a rolling programme of industrial action.
“We have a massive mandate for action which shows the anger of safety-critical staff across the rail network at attacks on their standards of living and the blunt truth is that this dispute could be settled for a fraction of the money being handed out in senior manager bonuses and to the train operators for not running services. That is a ludicrous situation which should never have been allowed to have arisen.
“With no shortage of cash in the bonus pot and to compensate the private train companies, it is no wonder that our members take the view that 1% is wholly inadequate and fails to recognise the massive pressures staff are working under to keep services running safely at a time when the company is generating profits of £1 billion.
“It is our members battling to keep Britain moving around the clock, often in appalling conditions, and they deserve a fair share from Network Rail for their incredible efforts.
“Our rail staff deserve a fair reward for the high-pressure, safety-critical work that they undertake day and night and the last thing that we need is a demoralised, burnt-out workforce living in fear for their livelihoods and their futures, and the message has come back loud and clear that that is exactly how they feel about the current offer from Network Rail.
“RMT remains available for talks and we hope that the company will appreciate the anger amongst staff at the current offer on pay and conditions from Network Rail and that they will agree to our call to come back to the table with an improved package.
“We expect rock-solid support for this action and will be taking a new campaign to the public under the banner ‘Our Jobs - Your Safety’ as we build support for the fight to stop this attack on a workforce whose core role is to deliver a safe railway to the British people.”
The RMT said NR generated profits of £1 billion last year, and was paying out £60 million in bonuses.
Each day of any strike would lead to NR paying compensation of £30 million to train companies, claimed the union.
The Transport Salaried Staffs Association, which also suspended a Bank Holiday strike, said it will ballot its members on the new pay offer.
TSSA official Lorraine Ward said: “With the expected cuts in the public sector from the new Tory Government, our members were as much concerned about job security as they were about pay.
“This offer means there will be no compulsory redundancies at NR for at least the next two years. Given the current climate, we think this is a major advance.”
The result of the ballot will be announced on June 13.
RMT members voted by 80% for strikes and 92% for other forms of industrial action, in a 60% turnout - all well above new thresholds being planned for union ballots by the Government.
The Queen’s Speech yesterday included a Bill which will require unions to achieve a turnout of at least 50% for a strike to be valid, while in transport, health, fire and education, 40% of those entitled to vote must back action.
Time limits will also be introduced on a mandate following a ballot for industrial action.
The Government said the aim of the Bill was to ensure that strikes are the result of “clear, positive and recent decisions” by union members as well as ensuring that disruption to essential public services had a democratic mandate.