The deal announced in Brussels provoked anger from the UK fishing industry, which will be subject to EU quotas throughout the 21-month transition period without British representation in setting quotas.
Fishing industry leaders accused the UK Government of trading away sovereignty over British waters during the transition phase, and Nicola Sturgeon leaped on what she called a "massive sellout" by the Conservatives.
In a joint press conference, Mr Davis hailed the agreement as confirmation that the UK could negotiate its own trade deals during the transition, which can be signed and implement the moment the 21-month period ends.
Despite being shorter than requested by the UK Government, Mr Davis said the implementation period ending in December 2020, was "near enough the two years we asked for".
On the border between Northern Ireland and the Republic, Mr Barnier said the two sides had agreed how the issue would be dealt with during the remaining negotiations.
He said they had agreed the EU's controversial "back stop position", which would see Northern Ireland effectively remain part of the single market if there was no wider agreement, would form part of the legal text of the withdrawal agreement.
"The backstop will apply unless and until another solution is found," he said, adding that because "nothing is agreed until everything is agreed", the UK's Brexit deal hung on whether that solution can be found by October.
In a major concession by the UK, Mr Barnier said that there had been "complete agreement" on future citizens' rights, including that EU citizens arriving in the UK during the transition period will be eligible for permanent residence on existing terms.
"British citizens and European citizens of the 27 who arrive during that transition period will receive the same rights and guarantees as those who arrived before the day of Brexit," he said.
Responding to the announcement on fishing, Scottish Fishermen’s Federation chief executive Bertie Armstrong said: “This falls far short of an acceptable deal. We will leave the EU and leave the CFP, but hand back sovereignty over our seas a few seconds later.
"Our fishing communities’ fortunes will still be subject to the whim and largesse of the EU for another two years.
“Put simply, we do not trust them to look after us. So we issue this warning to the EU: be careful what you do or the consequences later will be severe. To our politicians we say this: some have tried to secure a better deal but our governments have let us down.
“As a consequence, we expect a written, cast iron guarantee that after the implementation period, sovereignty will mean sovereignty and we will not enter into any deal which gives any other nation or the EU continued rights of access or quota other than those negotiated as part of the annual Coastal States negotiations.”
Ms Sturgeon tweeted: "This is shaping up to be a massive sellout of the Scottish fishing industry by the Tories. The promises that were made to them during #EUref and since are already being broken - as many of us warned they would be."