New legislation will mean that workers will not have to wait for 26 weeks to seek flexible arrangements, as set out under the current law.
The government also wants to introduce laws that make it easier for people on low incomes to get a second job.
However, the Trades Union Congress said the government must go "much further".
Flexible working has continued after the UK emerged from 1Covid1 lockdowns.
The Department for Business, Energy and Industrial Strategy (BEIS) said that if an employer cannot accommodate a request to work flexibly, it would have to discuss "alternative options" before rejecting it.
It said that flexible working did not just mean working from home but also included job-sharing, flexitime or staggered hours.
Peter Cheese, chief executive of the CIPD, which represents the human resources industry, said: "This new right will help normalise conversations about flexibility at the start of the employment relationship, with significant benefits for employees in terms of wellbeing and work-life balance."
The government also said it planned to remove "exclusivity clause restrictions" for workers on contracts who are paid £123 or less a week. It will allow people to work for multiple employers and take on second jobs.
The Trades Union Congress (TUC) said that flexible working kept "mums in work" and helped close the gender pay gap.
"But we'd like the government to go much further to ensure that flexible work now becomes the norm," said Frances O'Grady, general secretary of the TUC.
"Ministers must change the law so that every job advert makes clear what kind of flexible working is available in that role. And they should give workers the legal right to work flexibly from their first day in a job - not just the right to ask," she said.
The bill was introduced by Labour MP Yasmin Qureshi, who said that flexibility in the workplace was a lifeline rather than a "perk".
She said: "Younger families, single parents and lower earners have been hardest hit financially by the pandemic and the cost-of-living crisis.
"This makes it even more important for people who require it to be able to access flexible working."
The plans come as data from the Office for National Statistics suggests that record numbers of people are dropping out of the workforce due to ill health.
Flexible working offers a "much-needed pathway" in to the labour market by adjusting working patterns to support those who need it, added Labour MP Ms Qureshi.
As many firms struggle with recruiting amid record low unemployment, the government said the laws will "help businesses plug crucial staffing gaps by giving employers access to recruit from a wider talent pool".
Around 37% of working adults worked from home in 2020 during the height of the coronavirus pandemic. A number of firms, such as Lloyds Banking Group, have since introduced hundreds of roles that are now permanently done from home.
But others claim it makes staff unproductive and have ordered staff to return to the office.
In July, Sports Direct-owner Frasers Groups scrapped working from home. Meanwhile, the world's richest man, Elon Musk, has also told staff at Twitter and electric carmaker Tesla that working remotely is no longer acceptable.
The CIPD, however, said the new plans would make workplaces "more inclusive".
"[The plans will] improve access to flexible jobs for many people. Older workers, those with caring responsibilities and people with health conditions are among those who will particularly benefit," said Mr Cheese.
The new plans include allowing employees to make two flexible working requests in any 12-month period - currently they are allowed one.
It will also require employers to respond to requests within two months, down from three.
In addition, the government will remove the requirement on the employee to make suggestions as to how their flexible working request is dealt with by their employer.