Dividend stocks trading at discounted prices can make for great investments if you're willing to be patient. That's because, assuming their payouts are sustainable, you can lock in a higher yield than normal. You may also benefit from a rising share price in the future should their valuations recover.

Three dividend stocks that are cheap buys today, offer high yields, and could be good long-term plays include AstraZeneca (AZN -0.32%), ExxonMobil (XOM 1.20%), and Toronto-Dominion Bank (TD 0.60%). Here's a closer look at these three stocks and why you might want to consider adding them to your portfolio.

1. AstraZeneca

Healthcare company AstraZeneca provides investors with a dividend that yields 2.2%. That's higher than the S&P 500 average of 1.3%.

While the business possesses a diverse, robust portfolio with excellent long-term growth prospects, investors have been discounting it. The stock is trading near its 52-week low of $60.47, and its forward price-to-earnings (P/E) multiple (which is based on analyst expectations) is just over 14. That's cheap when you consider the average stock in the Health Care Select Sector SPDR Fund trades at a multiple of 20 times next year's earnings.

For a company such as AstraZeneca, which has generated more than $51 billion in sales over the trailing 12 months while averaging a profit margin of around 13%, this is not just a good dividend stock but also a solid growth stock to hang on to for the long haul. The company has been building up its drug portfolio over the years through acquisitions and in-house development. There are around 200 projects in the pipeline for this growth beast in therapeutic areas, such as oncology, cardiovascular, respiratory and immunology, and others.

AstraZeneca is a stock that can be suitable for any type of investor because it checks off a lot of boxes. It's a top healthcare stock you can buy and hold for years.

2. ExxonMobil

Investors can collect a higher yield with ExxonMobil, which currently pays 3.7%. The oil and gas giant has been known for decades to be a top dividend stock. The company's annual dividend has risen annually for 42 straight years, which is an impressive feat, given the volatility that often comes with commodity prices.

Earnings will fluctuate, but this can be a great way for investors to hedge against inflation and diversify their portfolios with a top oil and gas stock. Exxon got bigger and more efficient with its acquisition of Pioneer Natural Resources last year, which doubled its overall footprint in the Permian.

Exxon's stock is cheap, given its vast operations. In the trailing 12 months, the company has posted a profit of $33.7 billion on sales totaling $339.9 billion. The stock trades at a forward P/E multiple of 12 and can give investors good value for their money.

3. Toronto-Dominion Bank

Canadian-based Toronto-Dominion Bank, also known as TD Bank, is a top dividend stock investors can buy and hold for years and even decades. At 5.2%, it provides investors with a mouthwatering yield and doesn't come with much risk, either. It has been paying a dividend since 1857.

The company faced some adversity of late as it was hit with a $3 billion charge last year in relation to lax policies relating to money laundering in the U.S., where it's a top-10 bank. As a result, it now faces restrictions on growth in the U.S. market in the near term. While that isn't great news for investors, if you're planning on holding the stock for the long term, now can be an ideal time to do so -- when the market is feeling bearish on it.

TD is still a top bank stock and will likely remain that way for the foreseeable future. It's trading at a forward P/E of 10 and is just a few dollars away from its 52-week low. While it is facing some near-term headwinds, long-term investors could benefit from buying the stock now while its valuation is low.