* All three major U.S. stock indexes open at all-time highs

* U.S. Treasury yields tick higher; dollar wavers

* DAX hits all-time peak

* Trump signs $2.3 trillion spending package

* Brexit relief, vaccine roll-out also support sentiment

* 2020 asset performance http://tmsnrt.rs/2yaDPgn

NEW YORK, Dec 28 (Reuters) - All three major U.S. stock indexes opened at record highs on Monday, and Treasury yields rose as long-awaited stimulus and Brexit trade deals fueled investors' risk appetite.

U.S. equities followed their European counterparts higher in a broad rally, with small- and mid-cap stocks outperforming.

President Donald Trump reversed course on Sunday by signing a $2.3 trillion fiscal relief and spending package into law, heading off a potential government shutdown and setting the stage for Democrats in Congress to push for more robust $2,000 direct payments to millions of Americans.

"It's a positive tone to the U.S. market and part of that is the signing of the stimulus package by Trump, which appeared to be in doubt but has finally been accomplished," said Tim Ghriskey, chief investment strategist at Inverness Counsel in New York.

Britain reached a trade agreement with the European Union on Thursday, days before leaving one of the world's largest trading blocs, and urged businesses to prepare for disruptions resulting from the completion of Brexit.

"The Brexit deal is big news, and a big relief because it's dragged on for such a long time," Ghriskey added. "And we have a deal that everyone accepts, it's a good deal for everyone."

The Dow Jones Industrial Average rose 292.14 points, or 0.97%, to 30,492.01, the S&P 500 gained 33.39 points, or 0.90%, to 3,736.45 and the Nasdaq Composite added 70.75 points, or 0.55%, to 12,875.49.

European shares enjoyed their fourth straight session of gains following the U.S. stimulus and Brexit trade deals.

The ongoing rollout of coronavirus vaccines also buoyed sentiment, with Pfizer Inc announcing that it expects to complete distribution of 200 million doses in Europe by September.

Markets in Britain were closed on Monday in observance of the Boxing Day holiday.

The pan-European STOXX 600 index rose 0.73% and MSCI's gauge of stocks across the globe gained 0.59%.

Emerging market stocks lost 0.25%. MSCI's broadest index of Asia-Pacific shares outside Japan closed 0.17% lower, while Japan's Nikkei rose 0.74%.

U.S. Treasury yields crept higher and the yield curve steepened, stoked by risk-on sentiment in the wake of the stimulus bill becoming law.

Benchmark 10-year notes last fell 7/32 in price to yield 0.9531%, from 0.93% late on Thursday.

The 30-year bond last fell 25/32 in price to yield 1.6999%, from 1.666% late on Thursday.

The dollar slipped against a basket of world currencies as the euro gained strength as investors began pricing out Brexit risk.

The dollar index fell 0.12%, with the euro up 0.09% to $1.2215.

The Japanese yen weakened 0.28% versus the greenback at 103.80 per dollar, while Sterling was last trading at $1.3454, down 0.69% on the day.

Crude prices steadied as hopes for a demand rebound helped offset the prospect of increased OPEC+ output.

U.S. crude fell 0.21% to $48.13 per barrel and Brent was last at $51.35 per barrel, up 0.12% on the day.

Gold pared its early gains as the dollar recovered its losses amid the stocks rally.

Spot gold added 0.6% to $1,887.81 an ounce.

(Reporting by Stephen Culp; additional reporting by Danilo Masoni in Milan Editing by Paul Simao)