However, economists are concerned that the new business component of the index slipped to 53.3, its lowest level since summer 2016 in the aftermath of the Brexit referendum.
At 56.7 in September, up from 55.7 in August, the final IHS Markit Eurozone PMI Composite Output Index matched the earlier flash estimate. Forecasts were for a smaller decline to 56.4.
Any score of above 50 indicates growth, so this figure shows a steady expansion. In contrast, the Eurozone's manufacturing PMI rose to a 6½-year high of 58.1 during the same period.
Respondents are asked whether the situation has become better, worse, or has remained the same regarding parameters such as new orders and output.
At 3.45 am ET, IHS Markit is slated to release Italy's services PMI data.
Earlier, some mixed PMI data from the Euro-Zone left the Euro little changed.
But it also contained some discouraging signs: new orders increased at the weakest pace since August of previous year, inflation pressures rose at the fastest pace for several months and confidence sagged.
According to data published by IHS Markit, the UK's latest Service PMI rose from 53.2 to 53.6 in September, outpacing expectations that activity would remain flat last month, but still falling below the long-term average. New business orders were also down, with house building being the only bright spot.
"We still lean towards the Bank of England hiking interest rates from 0.25 per cent to 0.50 per cent in November, but the disappointing mix of higher inflationary pressures but slower economic activity in the September purchasing managers' surveys highlights the [Monetary Policy Committee's] dilemma", said Howard Archer of the EY Item Club.
IHS Markit said rising costs meant average prices in the United Kingdom were at their highest since April.
However, the United Kingdom still lags behind the eurozone, where services PMI grew strongly to 55.8 last month. However, despite having retreated by about 4.7% from August's 10-month highs due to sterling's BoE-led rally, the euro remains up 4% in the year to date against the British currency on the back of the diverging outlook for the two economies.