UPDATE 1-Markets bring forward ECB rate hike bets, see move before Draghi's term ends

* Investors bring forward bets on 1st ECB rate hike

* 10 bps point rate hike fully priced for Sept 2019

* ECB chief Draghi’s term expires in Oct 2019

* When will the ECB raise rates? (Updates with more details, comments chart)

LONDON, Sept 25 (Reuters) - Money markets now anticipate the ECB will lift interest rates in September 2019, bringing forward expectations for a first rate hike in a sign of growing conviction that a move will come before Mario Draghi’s term as ECB chief ends.

Draghi, whose term ends at the end of October 2019, predicted on Monday a “relatively vigorous” pick-up in underlying inflation, taken by some investors as a signal for a quicker pace in normalising policy.

Investors, who were pricing in a rate rise at the European Central Bank’s October 2019 meeting, as recently as a few days ago, now expect the first ECB hike since 2011 to be delivered earlier.

“You can downplay what Draghi said yesterday, but I think it was a notable shift in rhetoric,” said Martin van Vliet, senior rates strategist at ING.

The difference between the overnight bank-to-bank interest rate for the euro zone - known as Eonia - and forward Eonia rates dated for the ECB’s September 2019 meeting, was almost 10 basis points on Tuesday, up from around 8.5 bps last week.

That indicates investors are fully pricing in a 10 basis point rise in the ECB’s deposit rate -- the minimum it is likely to lift it by -- from minus 0.4 percent currently.

Money markets also price in roughly 17 basis points worth of ECB tightening by the end of 2019, which would be equivalent to almost two 10 bps point rate increases.

“That’s almost two rate hikes priced in for next year, which is quite a shift in pricing,” said Commerzbank rates strategist Michael Leister.

Euro zone bond markets have also sold off following Draghi’s comments on Monday, with 10-year German bond yields on Tuesday hitting four-month highs at around 0.55 percent.

That ratcheting up of ECB rate hike expectations comes just days before the central bank’s monthly asset purchases are set to drop by half to 15 billion euros.

The ECB’s 2.6 trillion euro ($3.06 trillion) stimulus scheme is expected to end at the close of this year and the ECB has said it expects rates to remain low through the summer of 2019.

For bond investors, the outlook for rates is now key, and a growing sense that the ECB will deliver its first hike of the cycle sooner rather than later comes as central banks globally head towards tighter monetary policy.

The U.S. Federal Reserve this week is widely tipped to hike rates for the third time this year and recent strong data has prompted expectations of more policy tightening in the year ahead.

According to Frederik Ducrozet, senior economist Europe at Pictet Wealth Management, around a third of global central banks are now hiking rates.

The rise in ECB rate hike bets in favour of September next year also reflects greater conviction that ECB chief Draghi will end his term with a rate hike.

The ECB last raised rates in 2011, under former President Jean-Claude Trichet, to pre-empt what turned out to be a phantom threat of inflation.

“If inflation unfolds as the ECB now forecasts, then it makes sense for markets to brace for the first rate hike before Draghi leaves,” said ING’s van Vliet.