While tobacco smoking has long been banned within Celtic Park, the deal with E-lites will allow pure nicotine to be legally consumed in the stands.
E-Lites, the biggest selling brand in the UK, said the green LED tip that glows when a user takes a puff on the device made it the "ideal" choice for the club and would help to differentiate the electronic cigarettes from tobacco products.
Campaigners said the move amounted to the industry attempting to normalise smoking again.
While some research points to electronic cigarettes being a valuable tool in reducing harmful tobacco intake, others claim the devices propagate addiction and support the tobacco industry.
Stewart Maxwell, MSP for West of Scotland, said: "I am very disappointed an extremely big and successful football club such as Celtic would get involved with this type of sponsorship deal.
"The whole campaign to ban smoking in public places was about de-normalising smoking as an activity in public. This (deal) goes exactly in the opposite direction.
"It sends out entirely the wrong message to young people."
While E-lites is not owned by a tobacco company, firms such as British American Tobacco have launched their own electronic cigarette, while Reynolds American, which owns the Camel brand, has also ventured into the market.
Mr Maxwell said: "The firms producing e-cigarettes often say they are offering a harm reduction product by helping people get off tobacco, as if they are being helpful. That is just not the case."
The Celtic deal comes as the electronic cigarette industry makes a number of inroads to clubs across the UK. E-Lites are being given to fans at the Derby County ground on some match days, while Merthyr Town Football Club in Wales renamed its ground the Cigg-e Stadium after its new sponsor.
Trevor Field, sales and marketing director from E-Lite, said:"We are proud to be able to offer Celtic supporters the opportunity to enjoy an alternative to smoking whilst watching the match."
E-cigarettes, which are cheaper than tobacco, turn nicotine and other chemicals into a vapour that is inhaled. They contain no tobacco, tar or carbon monoxide.
In Scotland, their popularity has forced companies such as ScotRail to ban their use on trains, while pub chain Wetherspoons is also amongst those who forbid their use.
From 2016 electronic cigarettes are to be licensed as a medicine and regulated as an aid to stop smoking from 2016. About 1.6 million people use them in the UK. The level of toxins is about one thousandth of those found in cigarette smoke.
Sheila Duffy, chief executive of Ash Scotland, said: "I am disappointed by the Celtic decision. Electronic cigarettes are much safer than tobacco, but they are produced by companies whose profit is money and these companies are looking for the next generation to provide that profit. E-lites is not owned by a tobacco company but the tobacco companies have an interest in promoting dual use.
"Addiction, in whatever form, is not a good state for people to be in."
A Celtic spokeswoman said: "Celtic's partnership is similar to that recently announced by a number of other football clubs."