Venus, 49, has been in caretaker charge since Tony Mowbray resigned on 29 September, during which time the Sky Blues have won twice in three matches.
But League One's bottom club have now given themselves three months to assess their position, based on results.
City have so far won just one of this season's 12 League One matches.
"The table doesn't lie," Venus told BBC Sport. "After a quarter of the season you can't just ignore it, but we do have to move on and try and change things for the better.
"It will take hard work and commitment but these players are capable of that."
After inspiring a 2-0 win in his first game in charge at Port Vale, Coventry were unsuccessful on Saturday, beaten 3-0 at Charlton.
But, having also enjoyed a 3-1 EFL Trophy win at home to Northampton, Venus now takes charge of his first home league game, against Oxford United on Tuesday.
The Hartlepool-born former Leicester City, Wolves, Ipswich Town and Cambridge United defender made 567 Football League appearances in a 19-year playing career.
All his time in management has been spent in coaching roles under Mowbray at Hibernian, West Bromwich Albion, Celtic and Middlesbrough.
When he then joined Mowbray at Coventry, it was in more of a senior scouting role as technical director - and he has spent time weighing up whether he wanted to return to more day-to-day coaching duties.
Since Coventry's relegation from the Premiership under Gordon Strachan in 2001, the Sky Blues have had 14 managers in just over 15 years.
Venus is the ninth since owners Sisu took over nine years ago, of which only Chris Coleman has taken charge of more than 100 matches.
Coventry City have asked caretaker boss Mark Venus to remain in charge until at least January, while they take their time over a longer-term appointment.