There's certainly evidence that thousands of German prisoners died from starvation after World War II. However, the precise number of people that died is a matter of some debate, as is whether the Allies (and Eisenhower in particular) can be blamed.

When planning for the occupation of Germany, the Allies initially set the ration scale for Germans at 2,600 calories per day, the same as in Belgium and France, and at the top of the scale considered adequate by the UN Relief and Rehabilitation Administration. However, the Allies had massively underestimated the extent of the damage to German infrastructure caused by the war and the ability of Germany to feed itself.

One of the most difficult questions was what to do with the (now disarmed and defeated) German military. They were entitled to certain protections under the 1929 Geneva Convention, but that convention was intended to apply to soldiers captured and held during wartime - not millions of defeated soldiers held within their home country. It was logistically impossible to feed all of these people at the level expected by the Geneva Convention (and that German POWs had been fed in camps in the UK, for example).

In March 1945, Eisenhower recommended creating a new class of prisoner - Disarmed Enemy Forces (DEFs). The message said:

The additional maintenance commitment entailed by declaring the German Armed Forces prisoners of war which would necessitate the provision of rations on a scale equal to that of base troops wold prove far beyond the capacity of  the Allies even if all German sources were tapped. ... Your approval is requested. Existing plans have been prepared upon this basis.

This proposal was approved, and upon victory the members of the defeated German military were declared DEFs not POWs. The UK adopted a similar maneuver, designating them as Surrendered Enemy Personnel (SEPs). By June 1945, there were approximately 3.4 million DEFs and SEPS, plus a further 4.2m POWs (those captured during the war itself). Most were kept in camps, with poor conditions and limited food. Around 1-2 million were held in a group of 19 camps called Rheinwiesenlager (the Rhine meadow camps). DEFs received around 1,200 to 1,500 calories per day. In 1969, the US Army Medical Department carried out a report on the conditions and concluded that this caloric intake was inadequate, and that lack of food in some cases led to "extensive malnutrition".

The number that died in Rheinwiesenlager (and other camps) from lack of food is a matter of debate. The official US statistics conclude that just over 3,000 died. German figures put the number at 4,537. One academic (R. J. Rummel) put the figure at 6,000.

The claim in your title comes from a book published in 1989 by Canadian historian James Bacque, Other Losses. He argued that the true number that died in Rheinwiesenlager and other camps was in the hundreds of thousands and may be as high as 1 million (approx 790,000 in the US camps, plus a further 250,000 in French camps). He specifically blamed Eisenhower's policies for these deaths, claiming that he kept the Germans on starvation rations even though there was enough food.

Other academics have severely criticised Basque's claims. Rummel wrote: "Bacque misread, misinterpreted, or ignored the relevant documents and that his mortality statistics are simply impossible." MacKenzie stated: "All in all, however, Bacque's thesis and mortality figures cannot be taken as accurate". Stephen Ambrose (biographer of Eisenhower) said that the research was:

flawed in its most fundamental aspects. … Mr. Bacque is wrong on every major charge and nearly all his minor ones. Eisenhower was not a Hitler, he did not run death camps, German prisoners did not die by the hundreds of thousands, there was a severe food shortage in 1945, there was nothing sinister or secret about the "disarmed enemy forces" designation or about the column "other losses."

On the basis of the current scholarship, I think we are on reasonably secure ground saying that the number of deaths in the camps was closer to 5,000 than 1 million. There does not seem to be any reasonable basis to claim that Eisenhower was personally responsible for these deaths. There was a huge food shortage in post-war Europe (and Germany especially) and it appears to have been a logistical impossibility to feed everyone at the level the Allies had originally planned for (2,600 calories).

Edited to make minor corrections and for formatting

Do you have a link to those NYTimes stories?