Gascoigne, who has battled alcoholism for many years, was fined £600 for one charge of assault and £400 for a drunk and disorderly charge.
The former Newcastle United and Tottenham Hotspur star was arrested after police were called to Stevenage station in Hertfordshire at around 10.30pm on July 4.
Security guard Jack Sherrington noticed that Gascoigne was staggering towards the railway tracks.
Staff tried to help him by putting him in a wheelchair, but he became abusive to Mr Sherrington and used the "c-word" repeatedly, Elaine McMillan, prosecuting, told Stevenage Magistrates' Court.
Ms McMillan said Gascoigne grabbed hold of Mr Sherrington in the neck area - an assault which lasted a few seconds.
Mr Sherrington, who was working for a company contracted to First Capital Connect, was uninjured.
The court heard that Gascoigne, of Gateshead, had been in Newcastle visiting his father, who has a heart condition. He was travelling from Newcastle to London King's Cross but got off at Stevenage.
The court heard that Gascoigne's ex-wife, Sheryl, and children were called to the station and, in her sentencing, Chair of the Bench Carolyn Marsh pointed out that his 17-year-old son was "distressed".
The 46-year-old, who received treatment for alcoholism in an American clinic earlier this year, was originally charged with two counts of assault, one involving his ex-wife, but that charge was dropped.
Gascoigne, clutching a packet of cigarettes and wearing a dark suit, pale blue shirt, beige loafers with no socks, and sunglasses, was greeted outside the court by a media scrum.
The packed courtroom looked on as Gascoigne listened to the charges being read to him and entered guilty pleas to assault and drunk and disorderly in a public place.
Gascoigne clutched his mobile phone throughout the court appearance.
His lawyer, Gavin Harris, said he had only consumed a small amount of alcohol due to a "combination of stress caused by worry for his father and acute pain from a hip operation six weeks previously".
Mr Harris said that because Gascoigne had not drunk alcohol for a significant period of time, the effects were stronger than would have otherwise been the case.
The court also heard that Gascoigne was receiving "one to one" treatment for his alcoholism, which is continuing.
With his sunglasses back on, Gascoigne left the court and was driven away in a grey Porsche.
In a statement outside court, Mr Harris said: "Mr Gascoigne has asked me to say a few words on his behalf.
"He wants to publicly apologise for his actions that evening.
"He now wishes to be left alone to carry on with his recovery."
He was also ordered to pay £100 in compensation to Mr Sherrington, court costs of £85 and a victim surcharge of £60.
A First Capital Connect spokesman said: "Violence towards any staff either in our direct employ or, as in this case, through a third party should not be tolerated and we welcome the court's decision."