The move came as the first-year passenger journey total for the Edinburgh-Tweedbank route was expected to top 1.4 million - around 20 per cent above target.
Mr Yousaf told The Scotsman said: "Performance on this line in my view has not been acceptable.
"I am pleased the ScotRail Alliance has put together an improvement plan.
"I will push them to do that as quickly as possible, and expect reliability to be significantly improved."
Scotland on Sunday revealed last month that train performance on the Â£350 million railway hit a new low at the beginning of August.
ScotRail figures showed only about one in four trains - 28.4 per cent - arrived on time.
Campaigners said their figures showed the situation was even worse and said the "shocking" number of delays and cancellations had reached "epidemic" proportions.
The improvements to be made include to the reliability of the Class 158 diesel trains which largely operate the route, which are ScotRail's worst performers.
There will also be work on the signalling system after faults with trackside axle counters, which detect where trains are on the line.
It is thought they may have been affected by weather conditions.
ScotRail Alliance managing director Phil Verster said: "It takes time for equipment to bed in - very often it does not work out of the box."
He also revealed that the current two-carriage trains that run most of the line's services would be replaced by three and four carriage trains to ease overcrowding when new trains arrive in two years' time.
Mr Yousaf and Mr Verster were speaking as they took part in a first anniversary celebration for the 35-mile line at Waverley Station in Edinburgh today, four days into its second year of operation.
Mr Yousaf added: "The Borders Railway - what a success it has been.
"The amount of benefit in economic and social terms has been outstanding, and outstripped our expectations."
The ScotRail Alliance, which includes track owner Network Rail, said the journey total hit hit 1 million in June after reaching 694,000 in March - 22 per cent above forecast.
Full year figures will not be available for several weeks, but The Scotsman understands that traffic has continued to be beyond targets, with the total expected to far exceed the 1.3m predicted - and it may approach 1.5m.
Rail consultant and Borders Railway campaigner David Spaven said the improvements were a start, but performance had also been affected the amount of double track on the line, enabling trains to pass each other, being cut back.
He said: "It is encouraging the transport minister has now acknowledged the scale of the reliability problem, and hopefully the ScotRail Alliance improvement plan will be able to deliver some worthwhile enhancement of performance.
"But sadly, due to Transport Scotland’s lack of strategic vision over the last five years, there are underlying problems with the line’s infrastructure and its Class 158 trains that cannot be fully resolved by any quick fix."