"has continued until today" is correct and usable in written English.
You can use this phrase to describe a situation that has remained unchanged over a long period of time or that started in the past and has continued up until the present day. For example: "The tradition of celebrating Christmas with family has continued until today."
Nestorianism has continued until today, though its adherents are few, with groups being found in Iraq, India, Iran, Syria, and North and South America.
Buddhist sway was introduced there early, during the reign of Aśoka Maurya (c. 269 232 bc); and, while on the subcontinent Buddhism prospered, declined, and finally disappeared, in Ceylon it has continued until today.
In fact, the number of all gun deaths started to rise precipitously beginning in 1986 and kept going up until 1994, when it began a decline that has continued until today, when gun homicides are down almost half from their peak.
At a Los Angeles news conference Friday, Insurance Commissioner Dave Jones said his department has evidence showing that the alleged illegal activity has continued until 2011.
… A Missouri judge has continued until next month the criminal case against New York Jets defensive lineman Sheldon Richardson, accused of resisting arrest and traffic counts for a summer police chase in suburban St . Louis
Economic advance and political stability would presumably have continued until today, had Mao not decided to throw everything into the melting pot again with his cultural revolution.The two key factors in the post-leap reconstruction were a change in leadership, in the sense that Mao took a back seat, and a change of policy.
The abuse was said to have begun in 1983 when the boy was 6 and to have continued until 1990.
The company, run by founder Stephen Marks, said the "challenging conditions" on the high street had continued until Easter.
This uplift trend may have continued until August 2013; however, after the 2007 event, deformation was aseismic.
Moreover, TFP growth seems to have continued until 1997, at which point the Asian economic crisis hit the Indonesian economy.
That campaign of asset sales has continued until as recently as this past weekend, when A.I.G. agreed to sell a majority stake in its enormous aircraft-leasing arm to a group of Chinese buyers for roughly $4.2 billion.
