Mr Swinney’s comments come after the First Minister said she would set out a legislative timetable for an independence referendum in the coming weeks.
Speaking to BBC’s Good Morning Scotland radio programme, Mr Swinney said it was ‘right’ to put forward preparations to enable the people of Scotland to decide their ‘constitutional future.’
The Deputy First Minister said: “What we’ve said all along is that when we get out of the intensity of Covid, we will start the preparations for the independence referendum and that’s exactly what the government has done.
"We took the sensible decision back in March 2020 to pause all preparations for an Independence Referendum despite having a mandate to do so.
"We now find ourselves in a position where we are in a much improved situation. We have very modest measure left in place to protect against Covid.”
Mr Swinney said the First Minister made clear that she will set out the preparations for a referendum which will take place before the end of 2023.
He added: "Obviously there is a variety of protocols that we have to follow, enabling the passing of legislation to take place in sufficient time for it to be understood by the public before a campaign period starts.”
Mr Swinney said a timetable for an independence campaign period is ‘being worked on’ in Government at the moment.
The Deputy First minister said: "We’ve just restarted the work on the independence preparations and as soon as the detail is formulated it will be shared with the public and with parliament.”
Mr Swinney acknowledged there has been ‘enormous disruptions’ to society as a result of the virus, however, said there was ‘a recovery underway’.
Asked if the campaign would take place before Scotland is fully recovered from Covid, Mr Swinney said: "We are making our recovery as we speak.
"There are business sectors that are in a stronger position today than they were pre-pandemic.
“We see the position on employment being strong within in Scotland with unemployment at a historic low.”
Speaking to the programme on Monday, Mr Swinney said today is a ‘significant moment of progress’ in tackling the virus as the final restrictions in Scotland are eased.
As of Monday, nightclubs are now able to reopen, while the caps on indoor events, table service requirements for venues selling alcohol and one metre social distancing will also be removed.
Ministers have also decided against extending the vaccine passport scheme to more hospitality settings ‘at this stage’.
However, Mr Swinney also told the programme that measures such as face coverings on public transport and public places and home working where appropriate will be in place for ‘some time to come’.
He said: "Covid is still out there. We can still see that there are thousands of cases on a daily basis in Scotland.”
Mr Swinney added that these measures are ‘sensible’ and ‘proportionate.’