It's understandable that many income investors search for ASX dividend shares that offer the safest streams of passive income.

For retirees and other investors who rely on dividend income to fund their living expenses, nothing is perhaps more important than having a good idea of what kind of paycheques one can expect over at least the next 12 months.

Unfortunately for us all, there's really no such thing as a 'safe' dividend share. No company is under any obligation to increase or even maintain a dividend payment from year to year. Or pay a dividend at all, for that matter – a lesson we all painfully learned during the pandemic.

But there are still shares that can come close. So today, let's talk about two of what I think are the safest dividend shares you can buy on the ASX today, judging by their records of paying out dividends for decades.

Wesfarmers may not exactly be a household name. But many of this sprawling retail and industrial conglomerate's underlying brands are. They include Bunnings, Kmart, OfficeWorks, Target, Kleenheat Gas, King Gee and many more.

Wesfarmers is one of the oldest shares of the Australian stock market. It has managed to change with the times over its long history but has also retained assets that continue to deliver growth to its portfolio.

Nowhere is this more evident than Wesfarmers' dividend track record. As an example, Wesfarmers paid out a total of $1.10 per share in dividends in 2009. By 2019, this had grown to $2.78 per share.

The company's more recent payouts have been diluted thanks to the Coles Group Ltd (ASX: COL) spinoff in 2018. But investors have still enjoyed a dividend pay rise every year since 2020, which is significant considering the impacts of the pandemic.

Today, Wesfarmers shares offer a fully-franked dividend yield of 2.92%.

Next up, we have one of my favourite ASX dividend shares in investing house Soul Patts.

Like Wesfarmers, Soul Patts is a highly diversified business. It owns a huge portfolio of underlying assets, which include a concentrated ASX stock portfolio. This is dominated by stakes in companies like TPG Telecom Ltd (ASX: TPG), New Hope Corporation Ltd (ASX: NHC) and Brickworks Ltd (ASX: BKW).

Soul Patts' assets also house a diversified, broader ASX stock portfolio, property, bonds, private credit and venture capital investments.

There may be no such thing as a safe dividend share, but in my view, Soul Patts is about as close as it gets. After all, this is a company with a 24-year and continuing streak of delivering annual dividend pay rises to its investors.

In 2012, this company gave its investors payouts worth a fully-franked 46 cents per share. But by 2023, that had risen to 87 cents per share.

Right now, Soul Patts shares are trading on a fully-franked dividend yield of 2.67%.