Mr Trump said that he did not believe Mr Biden was “monitoring” events in Ukraine late on Wednesday night, suggesting he was “probably sleeping” and lambasting him for his “stupidity and incompetence”.
Speaking moments after the first reports of Russian attacks, the former president said it would never have happened if he had been in office.
Mr Trump told Fox News: “I knew he [Putin] wasn’t going to be satisfied with a piece [of Ukraine] and now he sees the weakness, incompetence and the stupidity of this administration.
“As an American I’m angry about it and saddened by it. The whole thing should never have happened, and it would never have never happened during my administration.”
The comments came a day after Mr Trump referred to Mr Putin as a “tough cookie” and called his tactics “genius”.
The invasion reignited attacks by Republicans over Barack Obama’s meeting with then Russian President Dmitry Medvedev in 2012.
Mr Obama was caught on camera assuring Mr Medvedev that he would have “more flexibility” to deal with contentious issues like missile defence after the US presidential election,
Mr Obama, with Joe Biden as his vice-president, was attempting to “reset” ties between the former Cold War enemies.
At the time Mitt Romey, the Republican presidential nominee, accused the Obama administration of “pulling punches” on Russia.
A decade later Mr Biden was heavily criticised in the run-up to the invasion when he suggested Mr Putin would not be punished for a “minor incursion” into Ukraine.
He said that, if Vladimir Putin were to make only a “minor incursion,” then Russia would not face devastating sanctions.
The White House hurriedly corrected his comments, saying that by “minor incursion” Mr Biden meant Russian cyber attacks, rather than a small military invasion.